Question

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

Answer 1

Given: $x=\{1,3,5\},y=\{1,2,3\}$
$\therefore x\cap y=\{1,3,5\}\cap \{1,2,3\}$
Hence, $x\cap y=\{1,3\}$

Given: $A=\{a,e,i,o,u\},B=\{a,b,c\}$
$\therefore A\cap B=\{a,e,i,o,u\}\cap \{a,b,c\}$
Hence, $A\cap B=\left\{a\right\}$

Given: $A=\{x:x\text{is a natural number and multiple of}3\}$
$\therefore A=\{3,6,9,12,\dots \}$
$B=\{x:x\text{is a natural number less than}6\}$
$\therefore B=\{1,2,3,4,5\}$
$\therefore A\cap B=\{3,6,9,12,\dots \}\cap \{1,2,3,4,5\}$
Hence, $A\cap B=\left\{3\right\}$

Given: $A=\{x:x\text{is a natural number and}1<x\le 6\}$
$\therefore A=\{2,3,4,5,6\}$
$B=\{x:x\text{is a natural number and}6<x<10\}$
$\therefore B=\{7,8,9\}$
$A\cap B=\{2,3,4,5,6\}\cap \{7,8,9\}$
Hence, $A\cap B=\varphi$

Given: $A=\{1,2,3\},B=\varphi$
$\therefore A\cap B=\{1,2,3\}\cap \varphi$
Hence, $A\cap B=\varphi$