Introduction

Consider the sentences below:

  1. If I am bored, I go to a movie.
  2. Only If I am bored, I go to a movie.

The first sentence implies that whenever I feel bored, I go to watch a movie. But it is not necessary that if I went to for a movie, I was feeling bored. There could be some other reason as well. Feeling bored is one of the several reasons for which I go to a movie. 

On the other hand, the second sentence implies that if I went to watch a movie, I must be feeling bored. This means that feeling bored is the only reason for which I go to a movie.

So, we see that the sentences convey different meanings depending on how they are connected. In Logical Deduction, we draw a conclusion by understanding the logic of the premise (statement) given to us. 

Depending on how the sentences are connected, premises can of various types: 

Type 1: If A, then B

This means that A is one of the various conditions that lead to B. Imagine B as the destination and A as one of the several paths that lead to B.

If A, then B analogy image

As we can see, A is the sufficient condition for B, but it is not the necessary condition. There are other paths (conditions) that lead to B as well. 

Valid Conclusions:

  1. If A has happened, B has happened (because A leads to B).
  2. If A has not happened, B may or may not have happened (because A is not the only condition that leads to B).
  3. If B has happened, A may or may not have happened (again because A is not the only condition that leads to B).
  4. If B has not happened, A must not have happened (because if A happens, B has to happen).

Let’s look at some examples:

1. If it rains, the ground gets wet.

It means that whenever it rains, the ground gets wet but, the rain is not the necessary condition for the ground to get wet. It can get wet from other causes as well.

From this statement, we can infer that:

  • If the rain has occurred, the ground got wet.
  • If rain has not occurred, the ground may or may not be wet.
  • If the ground is wet, rain may or may not have occurred.
  • If the ground is not wet, the rain has not occurred.

2. If I listen to the radio, I enjoy myself.

From this statement, we can infer that:

  • If I listened to the radio, I must have enjoyed myself.
  • If I didn’t enjoy myself, I must not have listened to the radio.

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 I am bored, I seek my sister’s company.

A. I did not seek my sister’s company. 

B. I am bored.

C. I sought my sister’s company.

D. I am not bored.

From the given statement we can infer that:

1. If I am feeling bored, I will definitely seek my sister’s company. So, BC is logically correct.

2. If I am not seeking my sister’s company, I am definitely not bored. So, AD is also logically correct.

Therefore, the correct sequences are BC and AD.

Practice Exercise 2: Whenever I go to a movie, I take my sister along.

A. I went to a movie.

B. I took my sister along.

C. I did not go to a movie.

D. I did not take my sister along.

From the given statement we can infer that:

1. If I go to a movie, I will take my sister along with me. So, AB is logically correct.

2. If I did not take my sister along, I must not have gone to a movie. So, DC is also logically correct.

Therefore, the correct sequences are AB and DC.

Practice Exercise 3: If it is raining, then  I am indoors.

A. I am indoors.

B. I am not indoors.

C. It is raining.

D. It is not raining.

Clearly, both CA and BD are logically correct.

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