R K Bansal Solutions for Chapter: Sets, Exercise 1: EXERCISE

State whether or not the following sets are empty $:$

$\{\mathrm{prime} \mathrm{numbers} \mathrm{divisible} \mathrm{by} 2\}$

State whether or not the following sets are empty $:$

$\{\mathrm{negative} \mathrm{natural} \mathrm{numbers}\}$

Sate, giving reasons, Which of the following pairs of sets are disjoint sets and which are overlapping sets :

A = $\{$  Girls with ages below $15$ years $\}$ and

B = $\{$ Girls with ages above $15$ years $\}$

State, giving reasons, check whether the pair of sets are disjoint sets or overlapping sets :

$\mathrm{C}=\{$ Boys with ages above $20$ years $\}$ and

$\mathrm{D}=\{$ Girls with ages above $27$ years $\}$

State, giving reasons, which of the following pairs of sets are disjoint sets and which are overlapping sets $:$

$\mathrm{A} = \{\mathrm{Natural} \mathrm{numbers} \mathrm{between} 35 \mathrm{and} 60\}$ and

$\mathrm{B} =\{\mathrm{Natural} \mathrm{numbers} \mathrm{between} 50 \mathrm{and} 80\}$

Are the following pairs of sets are disjoint sets or overlapping sets? Give reasons.

$\mathrm{P} =\{\mathrm{Students} \mathrm{of} \mathrm{class} \mathrm{IX} \mathrm{studying} \mathrm{in} \mathrm{I}.\mathrm{C}.\mathrm{S}.\mathrm{E}. \mathrm{Board}\}$ and

$\mathrm{Q} =\{\mathrm{Students} \mathrm{of} \mathrm{class} \mathrm{IX}\}$

State, giving reasons, which of the following pairs of sets are disjoint sets and which are overlapping sets $:$

$\mathrm{A} =\{\mathrm{Natural} \mathrm{numbers} \mathrm{that} \mathrm{are} \mathrm{multiples} \mathrm{of} 3 \mathrm{and} \mathrm{less} \mathrm{than} 30\}$ and

$\mathrm{B} =\{\mathrm{Natural} \mathrm{numbers} \mathrm{divisible} \mathrm{by} 4 \mathrm{and} \mathrm{lying} \mathrm{between} 20 \mathrm{and} 45\}$

State, giving reasons, which of the following pairs of sets are disjoint sets and which are overlapping sets $:$

$\mathrm{P} =\{\mathrm{Letters} \mathrm{in} \mathrm{the} \mathrm{word} \text{'}\mathrm{ALLAHABAD}\text{'}\}$ and 

$\mathrm{Q} =\{\mathrm{Letters} \mathrm{in} \mathrm{the} \mathrm{word} \text{'}\mathrm{MUSSOORIE}\text{'}\}$