Question

the set (a union b complement) union (b intersection c) equals to​

Answer 1

Answer:

Step-by-step explanation:

Let a={1,2,3}

b={2,3,4}

c={3,4,5}

now

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

aU(b`)

b~={1,5}

aub~=(1,2,3,5}

binC={3,4}

(aUb~)U(binc)={1,2,3,4,5}

Answer 2

(A U Bᶜ) U (B ∩ C) = A U Bᶜ U C

Given:

The set expression (A U Bᶜ) U (B ∩ C)

To find:

(A U Bᶜ) U (B ∩ C) =

Concept:

• A U (B ∩ C) = (A U B) ∩ (A U C)

• S ∩ A = A, where S is universal set

• A U Aᶜ = S

Step-by-step explanation:

Now, (A U Bᶜ) U (B ∩ C)

= ((A U Bᶜ) U B) ∩ ((A U Bᶜ) U C)

• [ ∵ A U (B ∩ C) = (A U B) ∩ (A U C) ]

= (A U Bᶜ U B) ∩ (A U Bᶜ U C)

= (A U S) ∩ (A U Bᶜ U C)

• [ ∵ A U Aᶜ = S ]

= S ∩ (A U Bᶜ U C)

= A U Bᶜ U C

• [ ∵ S ∩ A = A ]

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