Question

If U = {2,3,5,7,9} and A = {2,3} , B = {2,5,7,9} then prove (I) (AUB)' = A'ΠB'
(ii)(AΠB)'= A'UB'

Answer 1

Answer:

U={2,3,5,7,9}

A={2,3}

B={2,5,7,9}

i) AUB={2,3,5,7,9}

(AUB)'=∅------- [1]

A'={5,7,9}

B'={3}

A'∩B'=∅---------- [2]

From [1 and [2],

we get (AUB)'=A'∩B'

ii) (A∩B)={2}

∴ (A∩B)'={3,5,7,9} ---- [1]

A'UB'={3,5,7,9}-----[2]

From [1] and [2],

We get (A∩B)'=A'UB'