Question

Set A and set B have 3 and 6 elements respectively what can be the minimum number of elements
in A ∪ B-
(a) 3 (b) 6 (c) 9 (d) 18

Answer 1

Answer:

The Correct Answer would be (b) = 6. The minimum number of elements that Set A∪B can have is 6, if set A and set B have 3 and 6 elements respectively.

Step-by-step explanation:

Given: No. of elements in Set A = 3 and Set B = 6

To Find: No. of elements in A∪B

We know from the formula for Union of sets:

                               n(A∪B) = n(A) + n(B) - n(A∩B)

Where, n(A∪B) = no. of elements in A∪B, n(A) = no. of elements in A, n(B) = no. of elements in B and n(A∩B) = n. of elements in both A and B.

Now, for the no. of elements in Union to be minimum, the smaller set should be contained in the bigger one, that is, it must be a subset (A⊂B). For this, no. of the elements of the bigger will be considered as smaller is totally included inside it.

Therefore, minimum number of elements in A∪B would be 6.