Single Choice

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

A$${ A }^{ C }\cup B\cup C$$
B$${ A }^{ C }\cup B$$
Correct Answer
C$${ A }^{ C }\cup C^{ C }$$
D$$A\cup B$$

Solution

Let $$S=(\mathrm{A}\cap \mathrm{B}^{C})^{C}\cup (B \cap C)$$ $$\Rightarrow S = (\mathrm{A}^{C}\cup \mathrm{B})\cup (B \cap C)$$ {De Morgan's Law} $$\Rightarrow S = \mathrm{A}^{C}\cup (\mathrm{B}\cup (B \cap C))$$ $$\therefore S = \mathrm{A}^{C}\cup \mathrm{B}$$

SIMILAR QUESTIONS

Sets, Relations and Functions

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