Question

A set $A$ has $3$ elements and another set $B$ has $6$ elements. Then

• A. $3≤n(A∪B)≤6$
• B. $3≤n(A∪B)≤9$
• C. $6≤n(A∪B)≤9$
• D. $0≤n(A∪B)≤9$

Answer 1

Answer: (C)

We have
$\min n(A∪B)=\max \{n(A),n(B)\}=\max \{3,6\}=6$
Max $n(A∪B)=n(A)+n(B)=9$;
$∴6≤n(A∪B)≤9$