Answer to Question #309897 in Discrete Mathematics for boi

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\$