adineo wrote:

I want to know why isnt 3 an inference.? Answer is only 1

Given : all A's are B's

So lets say, A's are apples and B's are fruits.

1. No A is not a B >> No apple is not fruit >> all apples are fruits >> satisfies

2. All B's are A's >> All fruits are apples >> certainly not true

3. Some B's are not A's >> Some fruits are not apples >> satisfies

Lets take another example, since we have alreday ruled out ans choice 2, we will not validate it with different example.

A = apple B = apple

1. No A is not a B >> No apple is not apple >> all apples are apples >> satisfies

3. Some B's are not A's >> Some apples are not apples >> not true

So 1 stands valid in all cases.

You can do the same using sets.

A = {1,2,3} and B = {1,2,3} OR B = {1,2,3,4}