Question

If $A=\{x:x\in I,-2\le x\le 2\}$,
$B=\{x:x\in I,0\le x\le 3\}$,
$C=\{x:x\in N,1\le x\le 2\}$ and
$D=\left\{\right(x,y):x,y\in N,x+y=8\}$, then

• A. $n(A\cup B\cup C)=5$
• B. $n\left(D\right)=7$
• C. $n(B\cup C)=5$
• D. none of these

Answer 1

Answer: (B)

$n\left(D\right)=7$

$A=\{-2,-1,0,1,2\}$,
$B=\{0,1,2,3\}$
$C=\{1,2\}$,
$D=\left\{\right(1,7),(7,1),(2,6),(6,2),(3,5),(5,3),(4,4\left)\right\}$
$\therefore A\cup B\cup C=\{-2,-1,0,1,2,3\}$
$B\cup C=\{0,1,2,3\}$
$n\left(D\right)=7$
Hence, option B.