Premises - Type 4: If A, then not B

In this case, A is the sufficient but not necessary condition for the non-occurrence of B.  Imagine B as the destination and A as one of the several paths that don’t lead to B. Now if you take the path A, you won’t reach B and if you reached B, you must not have taken the path A.

Logical Deduction: 'If A, then not B' analogy imageValid Conclusions:

  1. If A has happened, B does not happen.
  2. If B happens, A must not have happened.

Let’s look at some examples:

1. If I talk to my best friend, then I do not need to take a pill for a headache.

From this statement, we can infer that:

  • If I talked to my best friend, I did not need to take a pill for a headache.
  • If I took a pill for a headache, I must not have talked to my best friend.

2. If I take a cup of coffee, I do not feel sleepy.

From this statement, we can infer that:

  • If I took a cup of coffee, I won’t be feeling sleepy.
  • If I am feeling sleepy, I must not have taken a cup of coffee.

Your Turn:

Let’s practice what we have learned. Each question has a main statement, followed by four statements labeled A, B, C, and D. Choose the ordered pair of statements, where the first statement implies the second, and the two statements are logically consistent with the main statement.

Practice Exercise 1: If the employees are micromanaged, they do not perform well.

A. Employees are micromanaged.

B. Employees do not perform well.

C. Employees are not micromanaged.

D. Employees performed well.

Clearly, AB is logically correct. 

Also, we can infer that if the employees performed well, they must not have been micromanaged. So, DC is also logically correct. 

Therefore, the correct sequences are AB and DC.

Practice Exercise 2: Samanta will not eat the fruit if it is cherry.

A. The fruit is cherry.

B. The fruit is mango.

C. Samanta ate the fruit.

D. Samanta did not eat the fruit.

From the given statement we can infer that:

1. If the fruit is cherry, Samanta will not eat it. So, AD is logically correct.

2. If Samanta ate the fruit, it must not be cherry. But the fruit doesn’t need to be mango.

So, AD is the only correct sequence.

Practice Exercise 3: If you wear a sweater, you won’t feel cold.

A. You felt cold.

B. You did not wear a sweater.

C. You did not feel cold.

D. You wore a sweater.

Clearly, DC and AB are logically correct.