Question

Let N be the universal set and A, B, C, D be its subsets given by A={x:xisaevennaturalnumber},B={x:xNandxisamultipleof3} C={x:xNandx 5},D={x:xNandx  10} Find complements of A, B, C and D respectively.

Answer 1

`A^(')` = {1,3,5,7,9,....}

`B^(')` = {1,2,4,5,7,8,10,11,13,14......}

`C^(')` = {1,2,3,4,5}

`D^(')` = {10,11,12,13,14,15,......}

Explanation:

Solution:

It is given that, Universal set is the set of all Natural Numbers.

and

Set A, Set B, Set C, Set D are subsets of Universal set.

A = {x:x is even natural numbers} = {2,4,6,8,10,.....}

B = {x:x ∈ N and x is a multiple of 3} = {3,6,9,12,15,....}

C = {x:x∈ N and x < 5} = {6,7,8,9,10,.....}

D = {x:x ∈ N and x > 10} = {1,2,3,4,5,6,7,8,9}

U = {1,2,3,4,5,6,7,8,9,10,11,........}

Complements:

`A^(')` = U-A = {1,2,3,4,5,6,7,8,9,10,11,........} - {2,4,6,8,10,.....}

`A^(')` = {1,3,5,7,9,....}

`B^(')` = U-B = {1,2,3,4,5,6,7,8,9,10,11,........} - {3,6,9,12,15,....}

`B^(')` = {1,2,4,5,7,8,10,11,13,14......}

`C^(')` = U-C = {1,2,3,4,5,6,7,8,9,10,11,........} - {6,7,8,9,10,.....}

`C^(')` = {1,2,3,4,5}

`D^(')` = {1,2,3,4,5,6,7,8,9,10,11,........} - {1,2,3,4,5,6,7,8,9}

`D^(')` = {10,11,12,13,14,15,......}