If A and B are two given sets- thenA - A - Bc is equal to

We can solve the given expression by using laws of operations nbsp;on nbsp;sets as follows: A ∩ (A ∩ B)^c nbsp; =A ∩ (A^c ∪ B^c) nbsp; nbsp;[De Morg ...

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Standard XII

Mathematics

Intersection of Sets

If A and B ar...

Question

If $A$ and $B$ are two given sets, then
$A \cap (A \cap B)^{c}$ is equal to

$A$

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$B$

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$\emptyset$

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$A \cap B^{c}$

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Solution

The correct option is D
$A \cap B^{c}$

We can solve the given expression by using laws of operations on sets as follows:

$A \cap (A \cap B)^{c}$

$= A \cap (A^{c} \cup B^{c})$ $[De Morgan's law]$

$= (A \cap A^{c}) \cup (A \cap B^{c})$

$= ϕ \cup (A \cap B^{c})$

$= A \cap B^{c}$

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If A and B are two given sets, then A ∩ (A ∩ B)c is equal to

The correct option is D A∩Bc We can solve the given expression by using laws of operations on sets as follows: A ∩ (A ∩ B)c =A ∩ (Ac ∪ Bc) [De Morgan's law] =(A ∩ Ac) ∪ (A ∩ Bc) =ϕ ∪ (A ∩ Bc) =A ∩ Bc

If $A$ and $B$ are two given sets, then
$A \cap (A \cap B)^{c}$ is equal to

The correct option is D
$A \cap B^{c}$

We can solve the given expression by using laws of operations on sets as follows:

$A \cap (A \cap B)^{c}$

$= A \cap (A^{c} \cup B^{c})$ $[De Morgan's law]$

$= (A \cap A^{c}) \cup (A \cap B^{c})$

$= ϕ \cup (A \cap B^{c})$

$= A \cap B^{c}$