Using properties of sets show that (i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.

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Solution

(i)

From the distributive property:

A∪( B∩C )=( A∪B )∩( A∪C )

A∪( A∩B )=( A∪A )∩( A∪B ) =A∩( A∪B ) =A

Hence,

A∪( A∩B )=A

(ii)

From the distributive property:

A∩( B∪C )=( A∩B )∪( A∩C )

A∩( A∪B )=( A∩A )∪( A∩B ) =A∪( A∩B )

From part (i),

A∪( A∩B )=A

Hence,

A∩( A∪B )=A

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Similar questions

(i) A \cup (A \cap B) = A

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Using properties of sets, show that

(i) $A \cup (A \cap B) = A$ (ii) $A \cap (A \cup B) = A .$

A \cup (A \cap B) = A

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\begin{matrix} (i) A \cup (A \cap B) = A (i i) A \cap (A \cup B) = A \end{matrix}

(A \cup B) \cap (A \cap B') = A

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