Question

7.Assertion (A) If n(A) = 3 , n(B) = 6 and A is subset of B, then the number of elements in AUB is 9. Reason (R) If A and B are disjoint , then n(AUB) is n(A) + n(B).
(2 Points)​

Answer 1

Answer:

[math]0\le n(A\cap B)\le 3.[/math]

So [math]n(A\cup B)=n(A)+n(B)-n(A\cap B)\implies n(A\cup B) =9-n(A\cap B).[/math]

Minimum AUB elements condition: Out of 6 elements of set B, 3 elements are identical to that of set A. In this case AUB= B & it will have 6 elements

Maximum AUB elements condition: A & B are disjoint sets, that no element will be common to them. Then:

[math]n(AUB)= n(A) + n(B).[/math]

[math]AUB [/math] has 9 elements.

[math]\begin{align}\\\implies 0\ge -n(A\cap B)\ge -3\\\hline\\ \implies 9+0\ge 9-n(A\cap B)\ge 9-3\\\implies 9\ge 9-n(A\cap B)\ge 6 \\ \implies 9\ge n(A\cup B)\ge 6 \end{align}[/math]

Answer 2

Answer:

A is subset of B

B is subset of C

C is subset of A

then A=B=C

n(A)=3

n(B)=6

A is subset of B

n(AUB)=6

A and B are disjoint sets

n(AUB)=n(A)+n(B)

=3+6

=9