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Question

# Given the universal set = Universal ~set = {x:x∈ N and x<20} ~find: (i) A = {x:x=3p;p∈ N } (ii) B = {y:y=2n+3,n∈ N } (iii) C = {x:x is divisible by 4}

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Solution

## Universal set = {x:x∈ N and x<20} = {1,2,3,4,5,6,7,8,9,10,11,..........19} (i) A = {x:x=3p ; p ∈ N } x = 3p When P = 1, x=3× 1 = 3 When P = 2, x=3× 2 = 6 When P = 3, x=3× 3 = 9 When P = 4, x=3× 4 = 12 When P = 5, x=3× 5 = 15 When P = 6, x=3× 6 = 18 ∴ A = {3,6,9,12,15,18} Ans. (ii) B={y:y=2n+3,n∈ N } When n = 1, y=2× 1+3 = 2+3 = 5 When n = 2, y=2× 2+3 = 4+3 = 7 When n = 3, y=2× 3+3 = 6+3 = 9 When n = 4, y=2× 4+3 = 8+3 = 11 When n = 5, y=2× 5+3 = 10+3 = 13 When n = 6, y=2× 6+3 = 12+3 = 15 When n = 7, y=2× 7+3 = 14+3 = 5 When n = 8, y=2× 1+3 = 16+3 = 19 ∴ B ={5,7,9,11,13,15,17,19} Ans. ∴ C = {x:x divisible by 4} Ans. = {4,8,12,16} Ans.

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