Question

2
= (1.2.3.4.5). A = (2.4) and B = (3.4), then verify the following laws.
1.A-B = A n b 2.) (ANB)^-1 = A^-1UB^-1 iii) (AUB)^-1 = A^-1 n B​

Answer 1

Answer:

Step-by-step explanation:

Z={ 1,2,3,4,5}, A={2,4} ,B={3,4}

1. A-B= A∩B

A-B={2,4}-{3,4}={4}

A∩B={2,4} ∩ {3,4}={4}

Thus  A-B= A∩B

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2. (A∩B)'= A'UB'

A∩B={2,4} ∩ {3,4}={4}

so (A∩B)'= (1,2,3,5}

A'={ 1,3,5} and B'=(1,2,5}

A'UB'={ 1,3,5} U(1,2,5}={1,2,3,5}

Thus  (A∩B)'= A'UB'

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3} (AUB)' = A'∩ B'​

AUB = (2,4) U  (3,4)={2,3,4)

(AUB)'={1,5}

A'∩ B' ={ 1,3,5} ∩(1,2,5}={1,5}

Thus (AUB)' = A'∩ B'​

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