Question

State whether each of the following statement is true or false. Justify your answer.
$\left(i\right)\{2,3,4,5\}$ and $\{3,6\}$ are disjoint sets.
$\left(ii\right)\{a,e,i,o,u\}$ and $\{a,b,c,d\}$ are disjoint sets.
$\left(iii\right)\{2,6,10,14\}$ and $\{3,7,11,15\}$ are disjoint sets.
$\left(iv\right)\{2,6,10\}$ and $\{3,7,11\}$ are disjoint sets.

Answer 1

Given : $\{2,3,4,5\}$ and $\{3,6\}$
$\therefore \{2,3,4,5\}\cap \{3,6\}=\left\{3\right\}$
So, pair of set is not disjoint.
Given statement is false.

Given: $\{a,e,i,o,u\}$ and $\{a,b,c,d\}$
$\therefore \{a,e,i,o,u\}\cap \{a,b,c,d\}=\left\{a\right\}$
So, pair of set is not disjoint.
Given statement is false.

Given: $\{2,6,10,14\}$ and $\{3,7,11,15\}$
$\therefore \{2,6,10,14\}\cap \{3,7,11,15\}=\varphi$
So, pair of set is disjoint
Given statement is true.

Given: $\{2,6,10\}$ and $\{3,7,11\}$
$\therefore \{2,6,10\}\cap \{3,7,11\}=\varphi$
So, pair of set is disjoint.
Given statement is true