Question

Let $U=R($ the set of all real numbers $)$ If $A=\{x:x\in R,0<x<2\},B=\{x:x\in R,1<x\le 3\}$, then

• A. $A\cup B=${$x:x\in R$ and $0<x\le 3$}
• B. $A\cap B=${$x:x\in R$ and $1<x<2$}
• C. $A-B=${$x:x\in R$ and $0<x\le 1$}
• D. all of these

Answer 1

Answer: (D)

all of these

We have, $A^{\prime }=R-A=${$x:x\in R$ and $x\notin A$}

$=${$x:(x\in R$ and $x\ge 2)$ or $(x\in R$ and $x\le 0)$}

$=${$x:x\in R$ and $x\le 2$} $\cup${$x:x\in R$ and $x\le 0$}

Similarly, $B^{\prime }=${$x:x\in R$ and $x\le 1$} $\cup${$x:x\in R$ and $x>3$}

$\therefore A\cup B=${$x:x\in R$ and $0<x\le 3$}

$A\cap B=${$x:x\in R$ and $x<x<2$}

$A-B=${$x:x\in R$ and $0<x\le 1$}