Question

Find the correct answer?
$A - B = A \cap B' = B' - A'.$ True or false?
If true enter 1 else 0.

Answer 1

Hint: -To check this question whether it is true or false we will take help of venn diagram because using diagram it will be better to understand. We should know these results can be best explained by a venn diagram.

Complete step-by-step answer:
We have
A – B = It means we have to take all the elements of set A except elements of $\left( {A \cap B} \right)$
And it can be easily understood in a given diagram drawn.

Now we have
$A \cap B'$ = It means we have to take all the elements of set A except elements which are common with set B that are the same as the above condition .
This can also be easily understood in diagrams drawn.

At last we have
$B' - A' = $ It means we have to take all the elements of set A and not the elements of set A which are common to B that means indirectly it is saying the same thing as told in above two conditions.
And this also can be easily understood by drawing diagrams.

Hence all three are the same that means so this is true hence as told in question if it becomes true enter 1 so we will enter 1.

Note: - Whenever we get this type of question the key concept of solving is we have to understand set languages that understand the properties of sets to rearrange into easy form and also we should have good knowledge of venn diagrams to prove this question.