Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let A, B and C be sets. Then show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Let A, B and C be sets. Then show that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Answers (1)

Let x\in A\cap (B\cup C)

\begin{aligned} \Rightarrow & x\in A \text{ and } x\in (B\cup C) \\ \Rightarrow & x\in A \text{ and } x\in B\text{ or }x\in C \\ \Rightarrow & x\in A \text{ and } x\in B\text{ or }x\in A \text{ and } x\in C \\ \Rightarrow & x\in(A\cap B)\text{ or } x\in (A\cap C) \\ \Rightarrow & x\in (A\cap B)\cup (A\cap C) \\ \therefore & A\cap (B\cup C) \subset \ (A\cap B)\cup (A\cap C) & -(i) \end{aligned}

Let y\in (A\cap B)\cup (A\cap C)

\begin{aligned} \Rightarrow & y\in (A\cap B)\cup(A\cap C) \\ \Rightarrow & y \in (A\cap B)\text{ or }y\in (A\cap C) \\ \Rightarrow & y\in A\text{ and } y\in B\text{ or }y\in A\text{ and } y\in C\\ \Rightarrow &y \in A\text{ and }(y \in B\text{ or }y\in C) \\ \Rightarrow &y \in A\text{ and }(y \in B\cup C )\\ \Rightarrow &y \in A\cap(B\cup C ) \\\therefore & \ (A\cap B)\cup (A\cap C)\subset A\cap (B\cup C) & -(ii)\end{aligned}

From and (i) and (ii)

A\cap (B\cup C) =(A\cap B)\cup (A\cap C)

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question