Sets — MATHS STD 11 Science — Question

2. 6

Solution:

Let A be the left circle and B be the right circle.There are 3 elements in A and 6 elements in B.

The union of A and B contains elements that are in either circle.Thus,the union of A and B will be all of the elements in A along with all of the element B.

However, you have to subtract the elements that are in the overlapping area because you are counting twice.

If A and B don't overlap at all,then the union will ontain 9 elements.If A is completely inside B then the union will only contain 6 elements,which is the minimum no. of elements in the union of A and B.

let A = 1, 2, B = 2, 3

∴ A ∪ B = 1, 2, 3 which is 3 elements.

∴ A has 2 elements, B has 2 elements, and there is 1 element overlapping.

∴ 2 + 2 − 1 = 3! = 3 × 2 × 1 = 6