So far we’ve dealt with if then statements that are categorical: No Great White Sharks are vegetarians. Now we’re adding a level of complexity with some, all, and most. This level is called modality.
This video is 11 minutes long, and it’s all vital information. Below the video is a walkthrough of the content.
(3:08 in video) Negation of All
You would think the opposite of all would be none, but it isn’t. The opposite of all (which you are going to be using often on the LSAT if you are taking the contrapositive of an all statement) is some are not.
All means 100% of something.
Some means greater than 0% (none) but not 100% (all).
Some are not means below 100% (all) down to 0% (none).
Next LSAT: October 28th
(5:58 in video) Converse of All
Some are not means everything less than all, including nothing. So, on the LSAT, saying he has some are not winning lottery tickets in his pocket is perfectly valid (even if he has none).
- (5:58) Converse of All
The converse of All statements isn’t valid
All dogs (D) are nice animals (NA)
All D → NA doesn’t mean that nice animals are all dogs.
NA → D is invalid.
- The negation of All is Some Are Not.
The negation of All dogs are nice animals isn’t No dogs are nice animals, but “Some are Not”: Some dogs are not nice animals.
The opposite of nothing is some.
“Life is a great adventure or nothing”
The contrapositive (show in red above) shows that the opposite of nothing is something (the opposite of nothing isn’t everything).
(7:11) Modality w/Venn Diagrams
All grad students are higher-ed students.
Some grad students are on financial aid.
At Beverly Hills University,
no students are on financial aid.
Rule #1: All A are B
All LSATs are hard tests.
Some tests that are not hard are not an LSAT.
All hard tests are LSAT tests.
Some LSATs are not hard.
(maybe the June one?).
Rule #2: Some A are B
Some law school programs are part-time.
Valid Inference: Some B are A
Some part-time programs are law school programs.
Invalid Inference: Some A are not B
Some law school programs are not part-time.
Invalid Inference: Some B are not A
Some part-time programs are not law school programs.
Premise 1: Most voters view Hillary unfavorably.
Premise 2: Most voters view Trump unfavorably.
Choose the diagram that best represent the following statements.
All national scientists (S) are Ph.D. graduates (P), but not all Ph.D. graduates (P) are national scientists (S).
Answer: 2nd diagram. The statement claims that if you are a national scientist (S), then you have to be a Ph.D. graduate (P). The “X” should then be placed where it is both within the (S) and (P) circles. Both the first and second diagrams meet this criterion. However, the (S) circle should also be inside the (P) circle because the statement tells us that all (S) are (P). Therefore, the second diagram is the correct answer.
1st diagram. Although this diagram meets the criterion that “X” is both within the (S) and (P) circles, the whole (S) circle should be inside the (P) circle because the statement tells us that all (S) are (P). However, this diagram shows that some (S) are not (P), which is incorrect.
3rd diagram. This diagram does not show what the statement represents. The “X” should be placed where it is both within the (S) and (P) circles, but this diagram only shows “X” to be within the (S) circle and not the (P) circle. Therefore, this is not the correct answer.
Some animals (A) are not reptiles (R), but all reptiles (R) are animals (A).
Answer: 2nd diagram. The statement claims that there are animals that are not reptiles so the circle of animals (A) should have a part that does not intersect the circle of reptiles (R). Both the first and second diagrams meet this criterion, but the first one implies that there are reptiles that are not animals, which is wrong. The second best represents the statement that not all animals are reptiles because the whole (R) is inside (A), while not all (A) intersect (R).
1st diagram. Although this diagram meets the criteria that circle (A) should have a part that does not intersect circle (R), it shows that there are (R) that are not part of (A). Therefore, it is incorrect.
3rd diagram. This diagram does not show any intersection between circle (A) and circle (R), but the statement shows that all (R) are (A) and thus, should have an intersection. This diagram presents that there is no intersection between (A) and (R), which is incorrect.
Some of the members of the organization (M) are foreigners (F).
Answer: 1st diagram. The statement tells us some members of the organization (M) are foreigners (F). This means that there should be an intersection between the circle (M) and the circle (F). The first diagram shows exactly this relation, and it also shows that there are parts of (M) that are not part of (F) and there are parts of (F) that are not part of (M).
2nd diagram. This diagram shows the circle (M) and circle (F) are overlapping, which means that all (M) are (F), and all (F) are (M). However, the statement tells us that only some (M) are (F). Therefore, this is incorrect.
3rd diagram. This diagram shows that circle (M) and circle (F) have no intersection, but the statement claims that some (M) are (F), and thus, should have an intersection. Therefore, this is incorrect.
This can be a confusing question, but all it’s really asking you to do is use substitution (athletes for bankers).
The three dots symbolize the conclusion.
Next LSAT: October 28th