# Question of the Day! PrepTest 55, S.1, Q.15

A lot of people studying for the LSAT have troubles with inference questions. One question that was giving some of my students trouble is from Prep Test 55, Section 1, Question 15.

This question is about Zach’s Coffee Shop. (I cannot legally post the question unless I give licensing fees to LSAC). However, I am going to explain why each answer choice is wrong or right.

Analysis of the Question:  Zach’s coffeeshop has poetry readings almost every Wednesday. And then the question tells us that Every day that holds a poetry reading has 1/2 priced coffee.

We are looking for an inference – which is a statement that must be true based on a sentence or combination of sentences.

Therefore, something that MUST be true based on the stimulus is that – on the Wednesday’s with a poetry reading, the coffeeshop must offer 1/2 priced coffee. Let’s take a look at the answer choices to see if something matches our prediction.

(A) The stimulus does not tell us that Wednesday is the most common day to offer 1/2 priced coffee, since the stimulus does not tell us that they ONLY offer 1/2 priced coffee when there are free poetry readings. For all we know the coffeeshop offers 1/2 priced coffee everyday.

(B) Like A, the stimulus does not tell us that the coffeeshop only has poetry readings on Wednesday’s. Perhaps they have free poetry readings every single Friday.

(C) We know that: if there is a free poetry reading —> then there is 1/2 priced coffee. But, we cannot assume the reverse. We don’t know that every time there is 1/2 priced coffee there is also a free poetry reading. Be careful not to mix up necessary and sufficient conditions!

(D) CORRECT – We know that: Almost every Wednesday –> free poetry reading —> 1/2 priced coffee! Which is what this question is saying. If you were confused by the “most, if not all” part of the question, just note that — they could still offer 1/2 priced coffee on the Wednesday’s without poetry readings. They don’t have to have 1/2 priced coffee on those days, but they could offer it. That is why it is possible that they could offer 1/2 priced coffee on all Wednesdays. (“Almost every” means 51-99%, but since the 1% of days could still have 1/2 priced coffee for all we know – this answer choice is correct)

(E) Since we now understand why the coffeeshop could offer 1/2 priced coffee every Wednesday. This answer choice must be false, since we do not need to have a day without 1/2 priced coffee. (and “some” means – at least one)

# Formal Logic – Necessary & Sufficient?

One of the major concepts to understand on the LSAT is the use of formal logic. Formal logic is found predominantly in the Analytical Reasoning section of the LSAT, but it is also found in the Logical Reasoning section in inference questions and assumption questions.

Formal logic is founded on the understanding of necessary and sufficient assumptions. A necessary assumption is something that MUST be true, whereas a sufficient assumption is something that COULD be true. Formal logic is the use of rules to make deductions.

In the Analytical Reasoning section of the LSAT you want to diagram formal logic and necessary/sufficient problems. For If—then statements you want to diagram them as:

If A then B:         A —–> B

The left side of the arrow (A) is the sufficient condition, and then right side of the arrow is the necessary condition (B). Thus, it is possible for A to happen (although it doesn’t have to happen), but if A does happen then B MUST happen as well.

When you have a conditional statement you can also write the if—–then statement’s contra-positive. A contra-positive is just a further deduction that can be made from a conditional statement. To do this you will negate both terms and then flip them to the other side of the arrow.

If A then B:      ~B —-> ~A

Other Examples:

1) If not X then Y:      ~X —–> Y     OR     ~Y —–> X

2) if not S then not T:    ~S —-> ~T    OR    T —-> S

Another common type of formal logic seen on the LSAT is the “only if” statement.  For example, A only if B. Only if means that if A does happen then B must also happen. That means that:

A only if B can be rewritten as: if A then B:     A—–> B

Once again the contra-positive would be ~B —-> ~A

Another common type of formal logic seen on the LSAT is the “if and only if” and “if but only if” statements. “If and only If” is a bi-conditional logical connective between statements. This means that the truth of one of these statements requires the reverse to also be true. For example:

A if but only if B can be written as: if A then B AND if B then A:      A <—–> B

The contra-positive would be: ~A <—–> ~B

Also, the phrase “if and only if” means the same thing as “if but only if” in terms of formal logic and would be written the same way as the above example.

***”~” means NOT ***