Given that all A's are B's, which of the following

Question

Given that all A's are B's, which of the following inferences can be drawn?

1) No A is not a B
2) All B's are A's
3) Some B's are not A's

thanks

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

piyatiwari · Answer

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}

Maria240895chile · Answer

I was between 1 and 3, but I eliminate the 3rd option: Some B's are not A's >> maybe all B's are A's or just some of them, we have no enough info to determine it. The only option which is certainly true is 1

Given that all A's are B's, which of the following

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