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Model Paper 2 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 22 Marks
Question
If $A=\{a, b, c, d, e\}, B=\{a, c, e, g\}$ and $C=\{b, e, f, g\}$, verify that: $(A \cap B) \cap C=A \cap(B \cap C)$
✓

Answer

Suppose $x$ be any element of $(A \cap B) \cap C$
$\begin{array}{l}\Rightarrow x \in(A \cap B) \text { and } x \in C \\
\Rightarrow x \in A \text { and } x \in B \text { and } x \in C \\
\Rightarrow x \in A \text { and } x \in(B \cap C) \\
\Rightarrow x \in A \cap(B \cap C)\end{array}$
$\Rightarrow(A \cap B) \cap C \subset A \cap(B \cap C) \ldots( i )$
Now, suppose $x$ be an element of $A \cap(B \cap C)$
Then, $x \in A$ and $(B \cap C)$
$\begin{array}{l}\Rightarrow x \in A \text { and } x \in B \text { and } x \in C \\ \Rightarrow x \in(A \cap B) \text { and } x \in C \\
\Rightarrow x \in(A \cap B) \cap C \\
\Rightarrow A \cap(B \cap C) \subset(A \cap B) \cap C \ldots \ldots(\text { ii) }\end{array}$
Using (i) and (ii), we have $(A \cap B) \cap C=A \cap(B \cap C)$
Hence, proved.

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