If X and Y are two sets then X - Y - X- equals

Using Venn diagram nbsp; So nbsp;X ∩ (Y ∪ X)' is null set. nbsp; Alternative solution: X ∩ (Y ∪ X)' ⇒ nbsp;X ∩ (Y' ∩ X') ⇒ (X ∩ X') ∩ Y' ⇒ϕ∩ Y' ⇒ϕ ...

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Standard XII

Mathematics

Venn Diagrams

If X and Y ar...

Question

If $X$ and $Y$ are two sets then $X \cap (Y \cup X)^{'}$ equals

X

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Y

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ϕ

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none of these

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Solution

The correct option is C $ϕ$
Using Venn diagram

So $X \cap (Y \cup X)^{'}$ is null set.

Alternative solution:
$X \cap (Y \cup X)^{'}$
$\Rightarrow X \cap (Y^{'} \cap X^{'})$
$\Rightarrow (X \cap X^{'}) \cap Y^{'}$
$\Rightarrow ϕ \cap Y^{'}$
$\Rightarrow ϕ$

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If X and Y are two sets then X∩(Y∪X)′ equals

The correct option is C ϕUsing Venn diagram So X∩(Y∪X)′ is null set. Alternative solution: X∩(Y∪X)′ ⇒X∩(Y′∩X′) ⇒(X∩X′)∩Y′ ⇒ϕ∩Y′ ⇒ϕ

If $X$ and $Y$ are two sets then $X \cap (Y \cup X)^{'}$ equals

The correct option is C $ϕ$
Using Venn diagram

So $X \cap (Y \cup X)^{'}$ is null set.

Alternative solution:
$X \cap (Y \cup X)^{'}$
$\Rightarrow X \cap (Y^{'} \cap X^{'})$
$\Rightarrow (X \cap X^{'}) \cap Y^{'}$
$\Rightarrow ϕ \cap Y^{'}$
$\Rightarrow ϕ$