Question

Given the universal set = Universal ~set = $\{x:x\in Nandx<20\}$ ~find:

(i) A = $\{x:x=3p;p\in N\}$

(ii) B = $\{y:y=2n+3,n\in N\}$

(iii) C = $\{x:xisdivisibleby4\}$

Answer 1

Universal set = $\{x:x\in Nandx<20\}$ = $\{1,2,3,4,5,6,7,8,9,10,11,..........19\}$

(i) A = $\{x:x=3p;p\in N\}$ x = 3p

When P = 1, $x=3\times$ 1 = 3

When P = 2, $x=3\times$ 2 = 6

When P = 3, $x=3\times$ 3 = 9

When P = 4, $x=3\times$ 4 = 12

When P = 5, $x=3\times$ 5 = 15

When P = 6, $x=3\times$ 6 = 18 $\therefore$ A = $\{3,6,9,12,15,18\}Ans.$

(ii) $B=\{y:y=2n+3,n\in N\}$

When n = 1, $y=2\times$ 1+3 = 2+3 = 5

When n = 2, $y=2\times$ 2+3 = 4+3 = 7

When n = 3, $y=2\times$ 3+3 = 6+3 = 9

When n = 4, $y=2\times$ 4+3 = 8+3 = 11

When n = 5, $y=2\times$ 5+3 = 10+3 = 13

When n = 6, $y=2\times$ 6+3 = 12+3 = 15

When n = 7, $y=2\times$ 7+3 = 14+3 = 5

When n = 8, $y=2\times$ 1+3 = 16+3 = 19 $\therefore$ B =$\{5,7,9,11,13,15,17,19\}Ans.$

$\therefore$ C = $\{x:xdivisibleby4\}Ans.$ = $\{4,8,12,16\}Ans.$