Question

let a and b be sets. show that (a∩b)⊆a

Answer 1

Solution

Consider the two sets are

a = \left\{ {1,2,3,4,5,6,7} \right\}\ and b = \left\{ {5,6,7,8,9} \right\}\

Then

$\left( {a \cap b} \right) = \left\{ {1,2,3,4,5,6,7} \right\} \cap \left\{ {5,6,7,8,9} \right\}\\$

$\left( {a \cap b} \right) = \left\{ {5,6,7} \right\}$

We can see all the elements $5, 6, 7$ of set the $\left( {a \cap b} \right)$ are also present in the set a = \left\{ {1,2,3,4,5,6,7} \right\}\

Hence the set a \cap b\is a subset of the set a = \left\{ {1,2,3,4,5,6,7} \right\}\

We can write it mathematically as

\left( {a \cap b} \right) \subseteq a\