Formal vs. Informal Logic
Most Logical Reasoning questions use soft and fuzzy informal logic (with observations, lots of unstated assumptions, etc). Formal Logic is what a computer would do: hard, logic-following rules, like what you’ve done in this chapter. Formal logic is common in the legal field.
- You were on the neighbor’s property. (Premise)
- It is against trespassing laws to be on the neighbor’s property. (Premise)
- You are therefore guilty of trespassing. (Conclusion)
Not much wiggle room there! That’s why the LSAT often tests formal logic with must be true or must be false questions. We are dealing with certainty. Certainty is explored on the LSAT with Must Be True questions.
CHALLENGE: Identify Inferences
Must Be True (MBT) questions are about 7% of Logical Reasoning questions and are identifiable through their distinctive question stems:
- Which of the following must be false?
- If the statements above are true, which of the following must also be true?
- Which of the following may be correctly inferred?
- Which of the following inferences (inference means the same thing as “must be true” on the test) is best supported by the statement made above?
Conclusions differ from inferences in that conclusions are the result of premises and inferences must be true if the premises are true. Don’t panic if that sounds complicated; we review this concept extensively in the following chapter.
Must Be True are 7% of all Logical Reasoning questions.
How to solve
- Diagram out the statements of the argument (if you can’t get a quick grasp of it in your head).
- Make valid inferences from these statements (transitive property and contrapositive). Note any false inferences, if any, such as the Fallacy of the Converse and Fallacy of the Inverse.
- In Must be True questions you’ll find four choices that can sometimes be wrong and one that can never be wrong (that’s the correct choice!). Go through every answer choice systematically and check if it is ALWAYS true. These questions should always be tackled using PoE (Process of Elimination) method. If you can find a reasonable situation when it is not always true, eliminate it. Gradually eliminate answer choices until you have one left.
- 0:48 – The way to recognize if a question is a “must be true” question is to look for certain language cues, such as “must be true”, “can logically be inferred”, “can be properly concluded from the information given”, “consequence of the view above is”, and “must be true except”.
- 1:14 – The process that we recommend to better solve this type of questions is by first looking at related statements, identify the reasoning structure that connects these statements, then anticipate what the answer would be and review the answer choices.
- 1:43 – Let us take a look at an example. If we know that A → B and that B → C, we can then infer that A → C. We call this particular structure “syllogism”.
- 2:17 – Now, let us consider this example question involving “syllogisms”:
If there are any inspired performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be a sophisticated listener one must understand one’s musical roots.
- Question: If all of the statements above are true, which one of the following must also be true?
(A) If there are no sophisticated listeners in the audience, then there will be no inspired musical performances in the concert.
(B) No people who understand their musical roots will be in the audience if the audience will not be treated to a good show.
(C) If there will be people in the audience who understand their musical roots, then at least one musical performance in the concert will be inspired.
(D) The audience will be treated to a good show unless there are people in the audience who do not understand their musical roots.
(E) If there are sophisticated listeners in the audience, then there will be inspired musical performances in the concert.
- 2:37 – We can diagram the first statement as: Inspired Performance → Good Show. We can diagram the next statement as: Good Show → Sophisticated Listeners; and the last statement as: Sophisticated Listener → Understand Musical Roots.
- 2:53 – We can link these statements together to infer the following statement diagrams: Inspired performance → Understand Musical Roots; Inspired Performance → Sophisticated Listeners; Good Show → Understand Musical Roots; contrapositive: ~Understand Musical Roots → ~Good Show.
- 3:51 – Let us first look at answer choice (A). We can diagram this as: ~Sophisticated Listeners → ~Inspired Performance. This is the contrapositive of the inference of the first two statements. We will get back to this later.
- 4:10 – We can diagram answer choice (B) as: ~Good Show → ~Understand Musical Roots. This is a negation of the inference of the last two premises. Therefore, this is incorrect.
- 4:38 – Answer choice (C) can be diagrammed as: Understand Musical Roots → Inspired Performance. This is a reversal of the inference of all three statement, so this is incorrect.
- 4:58 – We can diagram answer choice (D) as: ~Good Show → ~Understand Musical Roots. This is exactly the same as answer choice (B) which is incorrect.
- 5:15 – Answer choice (E) can be diagrammed as: Sophisticated Listener → Inspired Performance. This is a reversal of the inference of the first and second premises, which means that it is incorrect.
- 5:28 – This leaves us answer choice (A) which is the correct answer.
- 5:58 – Here is an example of a “comparison” in conditional logic questions: City A is more populous than city B. City A is geographically smaller than city B. We can then infer the following statement: The population of City A is more dense than the population of City B. In this type of question, we want to look for how the comparisons among statements can work together such that we can infer new information from them.
- 6:25 – Let us take a look at this example involving “comparison”:
An advertisement states: Like Danaxil, all headache pills can stop your headache. But when you are in pain, you want relief right away. Danaxil is for you—no headache pill stops pain more quickly.
- Question: Evelyn and Jane are each suffering from a headache. Suppose Evelyn takes Danaxil and Jane takes its leading competitor. Which one of the following can be properly concluded from the claims in the advertisement?
(A) Evelyn’s headache pain will be relieved, but Jane’s will not.
(B) Evelyn’s headache pain will be relieved more quickly than Jane’s.
(C) Evelyn’s headache will be relieved at least as quickly as Jane’s.
(D) Jane’s headache pain will be relieved at the same time as is Evelyn’s.
(E) Jane will be taking Danaxil for relief from headache pain.
- 6:35 – The example given tells us that no headache pain pill stops more quickly than Danaxil. We can visualize this as: Danaxil ≤ Leading Competitor.
- 6:51 – We also know from the example that Evelyn will be taking Danaxil and Jane will be taking its leading competitor. We can then infer that Evelyn’s headache pain will be relieved at least as quickly as fast or faster than Jane’s.
- 7:16 – Answer choice (A) contradicts the information that the example tells us that all headache pills can stop their headache. Therefore, this is incorrect.
- 7:31 – Answer choice (B) is not the right answer because its claim is stronger than what the information supports. We do not know that Evelyn’s pain will be relieved more quickly. We only know that it will be relieved as quickly as Jane’s or maybe faster. This answer is simply too strong.
- 8:00 – Answer choice (C) gives us the weak inequality that the information provides. We will get back to this later.
- 8:12 – Answer choice (D) is stronger than what the information provides. This is one of the possibilities but not the only possibility. This answer is simply too strong and therefore, it is not the right answer.
- 8:29 – Answer choice (E) contradicts the information provided to us because it says that all headache pills can stop headache, so there’s no reason for Jane to exclusively take Danaxil to relieve her headache pain.
- 8:48 – Therefore, we are left with answer choice (C) as the correct answer.
- 9:04 – Let us take a look at an example that involves “causation”:
In a vast ocean region, phosphorus levels have doubled in the past few decades due to agricultural runoff pouring out a large river nearby. The phosphorus stimulates the growth of plankton near the ocean surface. Decaying plankton fall to the ocean floor, where bacteria devour them, consuming oxygen in the process. Due to the resulting oxygen depletion, few fish can survive in this region.
- Question: Which one of the following can be properly inferred from the information above?
(A) The agricultural runoff pouring out of the river contributes to the growth of plankton near the ocean surface.
(B) Before phosphorus levels doubled in the ocean region, most fish were able to survive in that region.
(C) If agricultural runoff ceased pouring out of the river, there would be no bacteria on the ocean floor devouring decaying plankton.
(D) The quantity of agricultural runoff pouring out of the river has doubled in the past few decades.
(E) The amount of oxygen in a body of water is in general inversely proportional to the level of phosphorus in that body of water.
- 9:30 – We can visualize the connection between these statements as follows: Agricultural Runoff → Phosphorus Levels Doubled → Increased Plankton → Less Oxygen → Fewer Fish. What we want to look for is information that can be determined based on this causal chain.
- 10:36 – If we visualize answer choice (A), it looks like the first three steps in the causal chain we made. Let us hold on this for now.
- 10:59 – Answer choice (B) is out of scope because it claims that before phosphorus levels doubled in the ocean region, most fish survived in the region. But we do not know what happened before phosphorus levels doubled, so this is not the right answer.
- 11:10 – Answer choice (C) claims that there would be no bacteria in the ocean if agricultural runoff ceased pouring out of the river, but we have no information about this. It is only a speculation about a hypothetical situation that we cannot prove so therefore, this is not the right answer.
- 11:28 – Answer choice (D) is not the right answer because it claims something that is stronger than the information provided.
- 11:41 – Answer choice (E) is a much stronger claim than what is provided to us. Therefore, it is not the right answer.
- 12:14 – We are then left with answer choice (A) as the correct answer, which is simply a part of the causal chain that is described in the stimulus.
- 12:24 – Note: Be wary of trap answer choices that may involve the scope, logic, or degree of the statements.
B. Must Be False
The opposite of Must Be True is Must Be False. In Must Be False questions you will find four choices that are correct and one choice that can never be correct. So, you just run through the choices with Process of Elimination to knock the four workable ones and select the one answer that can never work.
- 0:41 – In order to recognize “must be false” questions, we should look at the question stem and look out for certain phrases, such as “must be false”, “cannot be true”, and “could be true except”.
- 1:08 – The process that we recommend when working with this type of question is to first find the related statements, identify the reasoning structure that connects them, anticipate what the answer would be and navigate the answer choices carefully.
- 1:44 – Let us consider the following example:
Two things are true of all immoral actions. First, they are performed in public, they offend public sensibilities. Second, they are accompanied by feelings of guilt.
- Question: If all of the statements above are true, then which one of the following must be false?
(A) Some immoral actions that are not performed in public are not accompanied by feelings of guilt.
(B) Immoral actions are wrong solely by virtue of being accompanied by feelings of guilt.
(C) Some actions that offend public sensibilities if they are performed in public are not accompanied by feelings of guilt.
(D) Some actions that are accompanied by feelings of guilt are not immoral, even if they frequently offend public sensibilities.
(E) Every action performed in public that is accompanied by feelings of guilt is immoral.
- 3:09 – We can diagram the first part that is true of all immoral actions as: Immoral + Public → Offend.
- 3:24 – The second statement is not presented as a relationship but since we are talking about immoral actions, we diagram this as: Immoral → Guilt.
- 3:49 – Even though these statements don’t necessarily connect together, we can infer certain statements from them and anticipate possible answers.
- 4:20 – Answer choice (A) states that some immoral actions are not accompanied by feelings of guilt. This contradicts the second relationship. We will get back to this later.
- 5:00 – Answer choice (B) mentions something about when immoral actions are wrong. However, this was never mentioned in the statements. This choice is out of scope and thus, not the right answer.
- 5:13 – Answer choice (C) does not mention anything whether these actions are immoral actions. This means that this choice does not meet the sufficient condition of either of the two roles and cannot contradict either of them. This is an unsupported relationship and therefore, this is not the correct answer.
- 5:46 – Answer choice (D) mentions actions that are not immoral. This means that it does not meet the sufficient condition of either of the relationships and thus, cannot be the correct answer.
- 6:29 – Answer choice (E) is a modified version of a reversal of the second premise. Since it deals with a reversal, it does not contradict the original idea. Therefore, this is not the correct answer.
- 7:14 – We are then left with answer choice (A) as the correct answer.
- 7:31 – Let us consider another example that tackles “comparison”:
Sharks have a higher ratio of cartilage mass to body mass than any other organism. They also have a greater resistance to cancer than any other organism. Shark cartilage contains a substance that inhibits tumor growth by stopping the development of a new blood network. In the past 20 years, none of the responses among terminal cancer patients to various therapeutic measures has been more positive than the response among those who consumed shark cartilage.
- Question: If the claims made above are true, then each of the following could be true except:
(A) No organism resists cancer better than sharks do, but some resist cancer as well as sharks.
(B) The organism most susceptible to cancer has a higher percentage of cartilage than some organisms that are less susceptible to cancer.
(C) The substance in shark cartilage that inhibits tumor growth is found in most organisms.
(D) In the past 20 years many terminal cancer patients have improved dramatically following many sorts of therapy.
(E) Some organisms have immune systems more efficient than a shark’s immune system.
- 7:44 – We understand from the example that it is comparing sharks with other organisms. The best way to solve this is to track these comparisons being made.
- 8:06 – We can visualize the first statement regarding ratios as: Sharks (Cartilage/Mass) > Others (Cartilage/Mass).
- 8:12 – Similarly, the second statement can be visualized as: Sharks (Resist Cancer) > Others (Resist Cancer).
- 8:22 – The third statement tells us how sharks cancer resistance works, but it does not say anything about a comparison between Sharks and other organisms. We can simply ignore this one since it does not help us answer the question.
- 8:43 – The last statement is about patients and their response to shark cartilage compared to other treatments.
- 9:13 – We are looking for an answer choice that contradicts any of the premises.
- 9:20 – Answer choice (A) is incorrect because it contradicts the second premise. The second premise states that sharks resist cancer better than other organisms, but the second part of this choice claims that sharks’ resistance to cancer can be tied with other organisms. Since we are looking for a “must be false” answer, let us hold on to this for later.
- 10:00 – Answer choice (B) shows an unsupported relationship because it compares two non-shark organisms, which we can neither support nor contradict in this context. Therefore, this is not the right answer.
- 10:43 – Answer choice (C) is also an unsupported relationship because we cannot know based on the given premises whether it is true or not. Thus, this cannot be the right answer.
- 11:06 – Answer choice (D) does not necessarily contradict the statements. Even though patients are responding better to the shark cartilage therapies compared to other therapies, this does not mean that they’re not responding to those other therapies. This answer is too weak and therefore, not the right answer.
- 11:50 – Answer choice (E) is out of scope since immune systems were never discussed, so this is incorrect.
- 12:00 – Now we have answer choice (A) remaining as the right answer.
- 12:03 – Note: Be wary of trap answer choices that may involve the scope, logic, or degree of the statements.
Next LSAT: October 28th
Next LSAT: October 28th