Question

If $A$ and $B$ are finite sets and , ${A \subset B}$ then

• A. $n (A \cup B)\, =\, n(A)$
• B. $n (A \cap B)\, = \,n(B)$
• C. $n (A \cup B)\, =\, n(B)$
• D. $n (A \cap B) \,=\, \phi$

Answer 1

Answer: (C)

$n (A \cup B)\, =\, n(B)$

Answer 2

We have, $A \subset B$
$\therefore A \cap B=A \Rightarrow n(A \cap B)=n(A) \dots$(i)
Again, we know that
$n(A \cup B)=n(A)+n(B)-n(A \cap B)$
$\Rightarrow n(A \cup B)=n(A)+n(B)-n(A)$ [from E (i)]
$\Rightarrow n(A \cup B)=n(B)$