If A and B are any two sets, then A ∪ ( A ∩ B ) = ___. Options: A . &nbspA B . &nbspB C . &nbspAC D . &nbspBC

Answer: Option A : A If A and B are any two sets, then A ∩ B ⊆ A . Also, A ⊆ A ∪ ( A ∩ B ) ⇒ A ⊆ A ∪ ( A ∩ B ) ⊆ A ⇒ A ∪ ( A ∩ B ) = A

If A and B are any two sets, then A∪(A∩B) =&#

Question

If A and B are any two sets, then

A \cup (A \cap B)

= ___.

Options:

A . A

B . B

C . AC

D . BC

Answer: Option A
:
A
If A and B are any two sets, then

A \cap B \subseteq A .

Also,

A \subseteq A \cup (A \cap B)

\Rightarrow A \subseteq A \cup (A \cap B) \subseteq A

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

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