Q.3 Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(vi) { x : x is a perfect square }

(vii) { x : x is a perfect cube}

(viii) { x : x + 5 =8 }

(ix) { x : 2x + 5 =9}

(x) { x : x \geq 7 }

(xi) { x : x \inN and 2x + 1 > 10 }

Answers (1)

Universal set = U = {1,2,3,4,5,6,7,8.............}

(vi) { x : x is a perfect square }' = U - { x : x is a perfect square } =  { x : x \in N and x is not a perfect square }

(vii) { x : x is a perfect cube}' = U - { x : x is a perfect cube} =  { x : x \in N and x is not a perfect cube}

(viii) { x : x + 5 =8 }' = U - { x : x + 5 =8 } = U - {3} = { x : x\in N and x \neq 3 }

(ix) { x : 2x + 5 =9}' = U - { x : 2x + 5 =9} = U -{2} =  { x : x\in N and x \neq 2}

(x) { x : x \geq 7 }' = U -  { x : x \geq 7 } =  { x : x\in N and x < 7 }

(xi) { x : x \inN and 2x + 1 > 10 }' = U - { x : x \inN and x  > 9/2 } =  { x : x\in N and x \leq  9/2 }

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