Question

If u={1,2,3,4,5,67,8,9} A={2,4,6,8} and B={2,3,5,7}. verfiy that a) (AUB)'=A'nB' b)(AnB)=A'UB'​

Answer 1

Answer:

i) To Verify,

(AUB)' = A'nB'

L.H.S:

(AUB)'

(AUB) = {2,4,6,8} U {2,3,5,7}

= {2,3,4,5,6,7,8}

(AUB)' = U - (AUB)

= {1,9}

R.H.S:

A'nB'

A' = U - A

= {1,3,5,7,9}

B' = U - B

= {1,4,6,8,9}

A'nB' = {1,3,5,7,9} n {1,4,6,8,9}

= {1,9}

L.H.S = R.H.S

Thus, (AUB)' = A'nB'

ii) To Verify,

(AnB)' = A'UB'

L.H.S:

(AnB)'

(AnB) = {2,4,6,8} n {2,3,5,7}

= {2}

(AnB)' = U - (AnB)

= {1,3,4,5,6,7,8,9}

R.H.S:

A'UB'

A' = U - A

= {1,3,5,7,9}

B' = U - B

= {1,4,6,8,9}

A'UB' = {1,3,5,7,9} U {1,4,6,8,9}

= {1,3,4,5,6,7,8,9}

L.H.S = R.H.S

Thus, (AnB)' = A'UB'

Hence Proved

Step-by-step explanation:

Hope it Helps U

Answer 2

Answer:

There is a mistake in b question.The correct question is ( AnB)'=A'UB'

Anyway here is the answer.

Hope it helps!