Using properties of sets show that

(i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.

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Solution

(i) To show: A ∪ (A ∩ B) = A

We know that

A ⊂ A

A ∩ B ⊂ A

∴ A ∪ (A ∩ B) ⊂ A … (1)

Also, A ⊂ A ∪ (A ∩ B) … (2)

∴ From (1) and (2), A ∪ (A ∩ B) = A

(ii) To show: A ∩ (A ∪ B) = A

A ∩ (A ∪ B) = (A ∩ A) ∪ (A ∩ B)

= A ∪ (A ∩ B)

= A {from (1)}

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Similar questions

A \cup (A \cap B) = A

A \cap (A \cup B) = A

Using properties of sets, show that

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

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

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

\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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