Question

1. The figure given below reparents two solutions sets $P$and $Q$ on real number lines

Represent each of the following sets on different number lines

1. $P\cap Q$
2. $P\text{'}\cap Q$
3. $P\cap Q\text{'}$

Answer 1

Step 1: Find the set builder form of P of the number line

The set builder form is $P=\{x:-2<x\le 6,x\in R\}$ and $Q=\{x:2\le x<8,x\in R\}$ or $P=(-2,6]$ and $Q=[2,8)$.

Step 2: Find the solution set of $P\cap Q$ and draw on the number line

The solution set of $P\cap Q$ is $[2,6]$. and its representation on the number line is

Step 3: Find the solution set of $P\text{'}\cap Q$ and draw on the number line

The solution set of $P\text{'}\cap Q=Q-P$is $(6,8)$ and its representation on the number line is

Step 4: Find the solution set $P\cap Q\text{'}$ and draw on the number line

The solution set of $P\cap Q\text{'}=P-Q$ is $(-2,2)$and its representation on the number line is

Hence the solution set of

1. $P\cap Q$ is $[2,6]$
2. $P\text{'}\cap Q$ is $(6,8)$
3. $P\cap Q\text{'}$ is $(-2,2)$ and the representation on the number line is as shown above.