Question

If a and b are two sets then prove that a-b = a if and only if a intersection b is equal to null set

Answer 1

Answer:

let's take a={1,2,3} and b={4,5,6}

Step-by-step explanation:

Now

◆a intersection b={0} is null set

because in both set's no element is same.

....so a-b={a}....,

Answer 2

Explaination :

given : If a and b are two sets then prove that a-b = a if and only if a intersection b is equal to null set

solution:

Suppose A - B = A.

Assume p is an arbitrary element in the intersection of A and B; then p is in A and p is in B.

Since p is in A and A = A - B, we have p is not in B, contradicting our assumption

. Thus there are no elements in the intersection of A and B. That is, A (intersect) B is the null set.

hence , proved

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