There’s no denying that you need to learn Formal Logic before tackling the LSAT. But don’t worry, it will be easy and intuitive. We use interactive games to help teach students Formal Logic.

The most basic logic rule is the **Conditional **(which is a phrase in the form of A → B).

### 1. Translate Phrases Into Conditionals

The item on the left in an *If… then…* statement is called the **Sufficient** and the one on the right is the **Necessary**. The LSAT buries these conditionals in convoluted language. They are rarely stated bluntly as “*if… then….*“.

We can diagram **conditionals** by abbreviating the necessary and sufficient phrases and then using an arrow (→) to join them.

**[sufficient condition]** → **[necessary condition]**

### Conditionals Video Summary

- 00:24 – Mastering conditional logic is important for passing the LSAT since 38% of the “Logical Reasoning” questions use conditional statements or conditional logic.
- 00:52 – A conditional statement is in the form of
**X → Y**. - 1:08 – We call the left side of the conditional statement the “sufficient condition” and the right side the “necessary condition”.
- 2:15 – Solving causal arguments involves putting the statements into the form of a conditional statement (
**X → Y**). - 4:20 – The conditional statements in the “Logical Reasoning” section may take the form of a syllogism.

If**A → B**, and**B → C**, then**A → C** - 5:10 – LSAT questions revolve around taking away one of the parts of this syllogism and asking you to find it.

*“If you can dream it,*

*you can do it.”*

-Walt Disney

**DREAM → DO**

*“A person is not old until they let regrets*

*take the place of their dreams.”*

–John Barrymore

**O → LRTPD**

Next LSAT: November 25th

### 2. Necessary or Sufficient?

**Sufficient **

*Automatically **makes* something happens

**Necessary**

** Qualification** for something

### Necessary and Sufficient Conditions Part 1 Video Summary

- 00:15 – The premises of a causal argument provide support for the hypothesis that one event causes another.
- 1:08 – “Cause” is often used to describe something that has a specific outcome as a result.
- 2:12 – We can think of a “necessary cause” as an essential condition. It must be present for its corresponding conclusion to be present.
- 2:28 – A “sufficient cause” will always be enough to produce the effect. If it is present, then its corresponding conclusion must also be present.
- 5:58 – There are four possible combinations of necessary and sufficient conditions:
**necessary but not sufficient**,**sufficient but not necessary**,**both sufficient and necessary**, and**neither sufficient nor necessary**. - 6:52 – If P is necessary for Q, then Q cannot be true unless P is true. “
*Q is true only if P is true.*” This can be diagrammed as follows:**Q → P**. - 7:36 – If P is sufficient for Q, then P’s being true is enough to make Q true. “
*If P is true, then Q is true.*” This can be diagrammed as follows:**P → Q**.

### Necessary and Sufficient Conditions Part 2 Video Summary

- 00:26 – To say that P is a necessary condition for Q is to say that “
*Q is true only if P is true*”. This can be diagrammed as follows:**Q → P**. - 00:44 – To say that R is a sufficient condition for S is to say that “
*If R is true, then S is true*”. This can be diagrammed as follows:**R → S**. - 1:01 – There are four possible combinations of necessity and sufficiency:
**necessary and sufficient**,**necessary but not sufficient**,**sufficient but not necessary**, and**neither necessary nor sufficient**. - 4:27 – It is important to know this distinction because we tend to confuse these two.
- 6:13 – It is also important to know this distinction because they can help us figure out what things are.

#### Necessary, Sufficient, Both or Neither?

Identify whether each of the following statements presents a **necessary condition**, a** sufficient condition**, **both**, or** neither.**

- A
**necessary but not sufficient**condition is essential for the conclusion to be true but not enough to produce the effect on its own. - A
**sufficient but not necessary**condition is enough to produce the effect on its own but is not essential for the conclusion to be true. - A condition that is
**both sufficient and necessary**is essential for a conclusion to be true and enough on its own to produce the conclusion. - A condition that is
**neither sufficient nor necessary**is neither essential for a conclusion to be true nor enough on its own to produce the conclusion.

(Don’t make any extraordinary assumptions when answering these questions).

Watering a plant is _______________ for it to grow.

### Explanation

**Necessary but not Sufficient**

Watering a plant is a necessary but not sufficient condition for it to grow. It is necessary because water is required for plants to grow. However, it is not sufficient because it also needs other things for growth, such as sunlight and proper soil.

Finishing college is _______________ for one to be rich.

### Explanation

**Neither Necessary nor Sufficient**

Finishing college is neither necessary nor sufficient for being rich. Some people did not finish college but still became rich. Moreover, finishing college does not guarantee that a person will become rich.

Living in Hong Kong is _______________ for living in Asia.

### Explanation

**Sufficient but not Necessary**

Living in Hong Kong is a sufficient but not necessary condition for living in Asia. If one lives in Hong Kong, then it automatically means that they also live in Asia since Hong Kong is in Asia. However, it is not necessary because one can live in other countries in Asia other than Hong Kong.

Knowing the correct formula is _______________ for finding the volume of an object in the Math exam.

### Explanation

**Necessary but not Sufficient**

Knowing the correct formula is a necessary condition for solving the volume of an object in the math exam because using an incorrect formula will lead you to a wrong answer. However, it is not a sufficient condition because knowing the formula is not enough. You still have to do the calculation correctly to get the correct volume.

Reducing the usage of air conditioning in the house is _______________ for lowering the electricity bill.

### Explanation

**Sufficient but not Necessary **

Reducing the usage of air conditioning in the house is a sufficient but not necessary condition for lowering the electricity bill. It is sufficient because doing this will certainly lessen electricity consumption in the household and thus, lower the electricity bill. However, this is not a necessary condition since there are other ways to lower the electricity bill like limiting the use of other appliances or switching to cheaper alternatives.

Given that the passing score for the midterm science exam is 70%, getting a score of 70% or higher in the exam is _______________ for passing it.

### Explanation

**Necessary and Sufficient **

It is both necessary and sufficient that one gets a score of 70% or higher in the midterm science exam in order to pass it. It is a necessary condition because the passing score for the midterm science exam is precisely 70%, so getting 70% or higher is required for you to pass it. Moreover, it is also a sufficient condition because getting a passing score automatically means that you pass the exam.

For the average person, eating less is a _______________ for losing weight.

### Explanation

**Sufficient but not Necessary**

For the average person, eating less is a sufficient condition for losing weight since the food that one eats contribute to their weight. Thus, eating less is enough to lose weight. However, it is not a necessary condition because there are other ways to lose weight like exercising wherein one does not have to alter the amount of food they eat.

If the 3^{rd} digit of an item’s bar code is non-zero, then it is a _______________ that the 3^{rd} digit is less than nine.

### Explanation

**Neither Necessary nor Sufficient**

In this case, it does not matter whether the 3^{rd} digit of an item’s bar code is zero or not because the digits of its bar code being less than nine do not specifically infer whatever the condition for the nth digit of a bar code is. The 3^{rd} digit could be one, and it would fit the criteria of being non-zero and less than nine. Moreover, the 3^{rd} digit could be nine, and it would still fit the criterion of being non-zero but not the criterion of being less than nine. Therefore, it is neither necessary nor sufficient to infer that the 3^{rd} digit is less than nine given that the 3^{rd} digit of a bar code is non-zero.

If John usually leaves home at 8:30 am to not be late in his work which regularly starts at 9:30 am, given that his average daily commute time is 35 minutes, then it is a _______________ that he leaves at least five minutes earlier so he won’t be late to his work tomorrow morning if it will start at 9:00 am for tomorrow’s shift.

### Explanation

**Both Necessary and Sufficient**

The first thing that we should take note of is John’s average daily commute time of 35 minutes. If he usually leaves home at 8:30 am, then he will arrive in his office at around 9:05 am. The fact that his work regularly starts at 9:30 am is irrelevant to this problem. Now, if his shift for tomorrow will start at 9:00 am then it is both necessary and sufficient that he leaves at least five minutes earlier so he won’t be late. It is sufficient because given that the commute will take 35 minutes, leaving five minutes earlier (8:25 am) will allow him to arrive at work on time (9:00 am). Similarly, this is also a necessary condition. One may argue that he does not have to leave five minutes earlier since he can leave 20 minutes or five hours earlier. However, the phrase used is “at least five minutes” which covers all times greater than five minutes. Hence, John will not be late to his work tomorrow if and only if he leaves earlier for five minutes or more than usual.

# Necessary or Sufficient?

Total questions: 8

Quiz Length: 12 Minutes

Next LSAT: November 25th