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Sets — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSets3 Marks
Question
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that:
$(\text{A}\cap\text{B})'=\text{A'}\cup\text{B'}$
✓

Answer

$\text{A}\cap\text{B}=\{\text{x : x} \in \text{A and x }\in\text{B}\}$
$= \{2\}$
$\therefore(\text{A}\cap\text{B})'=\{\text{x}\in\text{U : x}\not\in\text{A}\cap\text{B}\}$
$=\{1, 3, 4, 5, 6, 7, 8, 9\}$
Also,
$\text{A}' ∪ \text{B}' = \{\text{x : x} \in \text{A' or x} \in\text{ B}'\}$
$=\{1, 3, 4, 5, 6, 7, 8, 9\}$
Hence, $(\text{A} \cap \text{B})' = \text{A}' \cup\text{ B}'=\{1, 3, 4, 5, 6, 7, 8, 9\}.$

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