Question

If n(A) = n(B) = 2 n(A intersection B) , then n(A union B) is a multiple of:​

Answer 1

Answer:

n(A)=m and n(B)=n ; then n(A×B)=mn.

What is the value of n(A×B)=mn. if m=6 and n

Answer 2

Answer:

n ( A ∪ B ) is a multiple of 3.

Step-by-step explanation:

Given :- n(A) = n(B) = 2 n( A ∩ B)

To Find :- n ( A ∪ B ) is a multiple of which number.

Solution :-

n( A) = n( B) = 2 n(A∩B )

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

Substituting the above given values, we get

n( A ∪ B ) = 2 n( A ∩ B ) + 2 n( A ∩ B ) - n( A ∩ B )

                = 4 n( A∩B ) -  n( A∩B)

                = 3 n(A ∩ B)

As n ( A ∪ B ) = 3 n(A ∩ B)

∴ n ( A ∪ B ) is a multiple of 3. Since 3 is a prime number so 3 doesn't have any factors.

∴ n ( A ∪ B ) is a multiple of 3 only.

#SPJ2

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