If $A \cup B=A \cup C$ and $A \cap B=A \cap C$, then

$B=C$ only when $A \subseteq B$

JEE MATHEMATICS MCQ: SET THEORY

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Analyzing +4 | -1

A \cup B=A \cup C

and

A \cap B=A \cap C

, then

View answer and explanation

Correct option: C

B=C

Option A (

A^{\prime}

) is correct because the expression

(A \cup B)^{\prime} \cup (A^{\prime} \cap B)

simplifies to

A^{\prime}

using set identities.

Practice All Chapter MCQs →

S

2 a_1 a_2 a_3 \ldots . . a_{2006}

a_1, a_2, a_3, \ldots ., a_{2006}

S

a N=\{a n: n \in N: b N=\{n b: n \in N\}

c N=\{c N: n \in N\}

b N \cap c N=d N

a, b, c \in N

b, c

A=\{x: x

\}

B=\{x: x

A-B

F(n)

n

[\mathrm{F}(20) \cap \mathrm{F}(16)] \subseteq \mathrm{F}(\mathrm{y})

40 \%

A, 20 \%

10 \%

C

A

C

4 \%

A

C

2 \%

A