Question

If A=(1, 3,5,7,11,13,15,17),B=(2,4,6....,18)and N is the universal set then find A'U((AUB) intersection B')

Answer 1

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Answer 2

Answer:

A'U[(AUB)nB'] = N

Step-by-step explanation:

A={1,3,5,7,11,13,15,17},

B={2,4,6,..,18}

N ={1,2,3,4,...}

i)A' = U - A

= {1,2,3,4,....}-{1,3,5,7,...,17}

={2,4,6,8,10,12,14,16,18,...}

ii)AUB={1,3,5,7,11,13,15,17}

U{2,4,6,..,18}

={1,2,3,4,5,6,7,8,...,17,18}

iv) B' =U-B

= {1,2,3,...}-{2,4,6,....,18}

= {1,3,5,...,17,19,20,21,...}

v)(AUB)nB'

= {1,2,3,4,....18}n{1,3,5,...,17,19,20,...}

={1,3,5,....,17}

iii) A'U[(AUB)nB']

={2,4,6,8,10,...16,18,...}U{1,3,5,...,17}

= {1,2,3,5,6,....,}

=N

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