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RRB Technician Grade 1 Model Paper 1

Question : 47 of 100

Marks: +1, -0

If A and B are two sets, then A ∩ (A ∪ B) equals

Solution:

Concept:

Use the distributive law of set intersection over union to simplify

A \cap (A \cup B)

Explanation:

According to the distributive law,

X \cap (Y \cup Z) = (X \cap Y) \cup (X \cap Z)

Here, take

X = A

Y = A

, and

Z = B

So,

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

Since

A \cap A = A

, the expression becomes

A \cup (A \cap B)

The set

A \cap B

is always a subset of

A

Therefore, the union

A \cup (A \cap B)

contains no elements outside

A

and simplifies to just

A

Thus,

A \cap (A \cup B) = A

Answer:

A

(Option A).

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