Premises - Type 6: Either A or B

In this case, one of A or B happens. If one happens, the other does not happen.

Valid Conclusions:

  1. If A happens, B does not happen.
  2. If A does not happen, B happens.
  3. If B happens, A does not happen.
  4. If B does not happen, A happens.

Let’s look at some examples:

1. I drink either coffee or juice.

From this statement, we can infer that:

  • If I drank coffee, I wouldn’t have drunk juice.
  • If I didn’t drink coffee, I would have drunk juice.
  • If I drank juice, I wouldn’t have drunk coffee.
  • If I didn’t drink juice, I would have drunk 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: Either the orangutan is not angry, or he frowns upon the world.

A. The orangutan frowns upon the world.

B. The orangutan is not angry.

C. The orangutan does not frown upon the world.

D. The orangutan is angry.

From the given statement we can infer that:

1. If the orangutan is angry, he frowns upon the world. So, DA is logically correct.

2. If the orangutan is not angry, he does not frowns upon the world. So,  BC is also logically correct. 

3. If the orangutan frowns upon the world, he must be angry. So, AD is also logically correct.

4. If the orangutan does not frown upon the world, he must not be angry. So, CB is also logically correct.

Therefore, the correct sequences are DA, BC, AD, and CB.

Practice Exercise 2: Either Sam is ill, or he is drunk.

A. Sam is ill.

B. Sam is not ill.

C. Sam is drunk.

D. Sam is not drunk.

From the given statement we can infer that:

1. If Sam is ill, he must not be drunk. So, AD is logically correct.

2. If Sam is not ill, he must be drunk. So, BC is also logically correct.

Similarly, DA and CB are also logically correct.

Therefore, the correct sequences are AD, BC, DA, and CB.

Practice Exercise 3: Either the train is late, or it has derailed.

A. The train is late.

B. The train is not late.

C. The train is derailed.

D. The train is not derailed.

Clearly, AD, DA, BC, and CB are logically correct.