Question

If n(A) =8 and n(B) =5, then minimum number of elements in AUB​

Answer 1

Answer:

Given n(A) = 8

n(B) = 5

Then maximum number of elements in n(AUB) = 8 + 5 = 13

Answer 2

Minimum number of elements in A ∪ B = 8

Given :

n(A) = 8 and n(B) = 5

To find :

The minimum number of elements in A ∪ B

Solution :

Step 1 of 2 :

Write down the number of elements in the given sets

Here the given sets are A and B such that n(A) = 8 and n(B) = 5

Step 2 of 2 :

Calculate minimum number of elements in A ∪ B

We are aware of the formula on set theory that ,

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Now n(A ∪ B) will be minimum when n(A ∩ B) is maximum

Again n(A ∩ B) is maximum when n(A ∩ B) = n(B)

⇒ n(A ∩ B) is maximum when B ⊆ A

Thus for B ⊆ A we have ,

n(A ∪ B)

= n(A) + n(B) - n(A ∩ B)

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

= n(A)

= 8

Hence minimum number of elements in A ∪ B = 8

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