# 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  7 }(xi) { x : x N and 2x + 1  10 }

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  N and x is not a perfect square }

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

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

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

(x) { x : x  7 }' = U -  { x : x  7 } =  { x : x N and x  7 }

(xi) { x : x N and 2x + 1  10 }' = U - { x : x N and x   9/2 } =  { x : x N and x   9/2 }

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