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Sets Practice Test 1

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Question : 10 of 33

Marks: +1, -0

If P and Q are two sets and P′ denotes thecomplement of P, then (X ∪ (X ∩ Y )′)′:

X
ϕ
Y
Y′
None of these

Solution: 👈: Video Solution

Concept:

Use De Morgan’s Law and the double complement rule to simplify the set expression.

Explanation:

By De Morgan’s Law,

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

.

So,

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

.

The double complement gives

((X \cap Y)')' = X \cap Y

.

Therefore, the expression becomes

X' \cap (X \cap Y)

.

Rearrange:

(X' \cap X) \cap Y

.

Since

X' \cap X = \phi

, we get

\phi \cap Y

.

Hence, the final value is

\phi

.

Answer:

\phi

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