Single Choice

If $$X$$ and $$Y$$ are two sets, $$X\cap { \left( Y\cup X \right) }^{ C }$$ is equal to

A$$X$$
B$$Y$$
C$$\phi $$
Correct Answer
D$$X\cap Y$$

Solution

$$X\cap (Y\cup X)^{C}=X\cap (Y^{C}\cap X^{C})$$ $$=(X\cap Y^{C})\cap (X\cap X^{C})$$ $$=(X\cap Y^{C})\cap \phi $$ $$=\phi $$

SIMILAR QUESTIONS

Sets, Relations and Functions

The set $$\left( A\cap { B }^{ C } \right) ^{ C }\cup \left( B\cap C \right) $$ is equal to

Sets, Relations and Functions

Let $$A$$ and $$B$$ be two sets then $$\left( A\cup B \right) '\cup \left( A'\cap B \right) $$ is equal to

Sets, Relations and Functions

If $$U=\{1,2,3,4,5,6, 7, 8, 9 \}, A = \{2, 4, 6, 8\} $$ and $$B = \{ 2, 3, 5, 7\}.$$ Verify that (i) $$(A \cup B)' = A' \cap B'$$ (ii) $$(A \cap B)' = A' \cup B'$$

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