Question

Find the intersection of each pair of sets:
(i) X={$1,3,5$} Y={$1,2,3$}
(ii) A={$a,e,i,o,u$} B={$a,b,c$}
(iii) A={$x:x$ is a natural number and multiple of $3$}
B={$x:x$ is a natural number less than $6$}
(iv) A={x:x is a natural number and $1<x\le 6$}
B={x:x is a natural number and 6 < x < 10}
(v) A={1,2,3}, $B=\varphi$

Answer 1

(i) $X=\{1,3,4\},Y=\{1,2,3\}$
$X\cap Y=\{1,3\}$
(ii) $A=\{a,e,i,o,u\},B=\{a,b,c\}$
$A\cap B=\left\{a\right\}$
(iii)$A=\{x:x\text{is a natural number and multiple of 3}\}=\{3,6,9....\}$
$B=\{x:x\text{is a natural number less than 6}\}=\{1,2,3,4,5\}$
$\therefore A\cap B=\left\{3\right\}$
(iv) $A=\{x:x\text{is a natural number and}1<x\le 6\}=\{2,3,4,5,6\}$
$B=\{x:x\text{is a natural number and}6<x<10\}=\{7,8,9\}$
$A\cap B=\varphi$
(v) $A=\{1,2,3\},B=\varphi$
$A\cap B=\varphi$