Question

Let A={x:x€W, x<5},B={x:x is an prime number less than 5} and U={x:x is an integer, 0≤x≤}. verify (AUB)'=A'nB'​

Answer 1

SOLUTION

GIVEN

• A = { x : x ∈ W, x < 5 }

• B = { x :x is an prime number less than 5}

• U = { x : x is an integer, 0 ≤ x ≤ 5 }.

TO VERIFY

( A U B )' = A' ∩ B'

EVALUATION

Here

A = { x : x ∈ W, x < 5 }

= { 0, 1, 2, 3, 4 }

B = { x : x is an prime number less than 5 }

= { 2, 3 }

U = { x : x is an integer, 0 ≤ x ≤ 5 }

= { 0, 1, 2, 3, 4, 5 }

∴ ( A U B )

= { 0, 1, 2, 3, 4 }

∴ ( A U B )' = { 5 }

Again

A' = { 5 }

B' = { 0, 1, 4, 5 }

∴ A' ∩ B' = { 5 }

∴ ( A U B )' = A' ∩ B'

Hence verified

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