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Question

Let A and B be two sets having 4 and 8 elements respectively. Write the minimum number of elements that AB can have.


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Solution

Given, a set A having 4 elements i.e. n(A)=4

Set B having 8 elements i.e. n(B)=8

We know that n(AB)=n(A)+n(B)-n(AB)..........(1)

From the formula, we can say that AB having the minimum number of elements when AB having the maximum number of elements.

Since n(A)=4 and n(B)=8, therefore the maximum number of elements in AB are 4.

Substitute all the values in the equation (1), and we get;

n(AB)=4+8-4=8

Therefore the minimum number of elements that AB can have is 8.


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