Question

If A and B are sets then find A∩(B∪A)c from the given Venn diagram.

Options are given below, please let me know the best answer for this.

1) Ac∪Bc

2) B

3) Empty Set

4) AUB

Answer 1

Given : A and B are sets

To Find :   A ∩ ( B ∪ A )

A ∩ ( B ∪ A )'

Solution:

A ∩ ( B ∪ A )'

= A ∩ ( B' ∩ A ')

= (A ∩ A ') ∩  B'

A ∩ A ' =  Empty set = ∅

= ∅ ∩  B'

= ∅

A ∩ ( B ∪ A )' = Empty set

A ∪ B  Means  x : x ∈ A  or x ∈ B

A ∩  B  Means  x : x ∈ A ,B

A ∩ ( B ∪ A )

=> B ∪ A Means  x : x ∈B  or x ∈ A

A ∩ ( B ∪ A )

=> x : x ∈  A  , (B or A)

=> x ∈  A

=> A ∩ ( B ∪ A )   = A

A ∩ ( B ∪ A )   = A

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