Question

State, whether the following pairs of sets equal or not:

M = {x :x $\in$W and x + 3 <8} and N = {y : y = 2n -1, $\in$ N and n < 5}

Answer 1

Step : Check whether the given pair of sets are equal
Given, M = {x :x $\in$W and x + 3 <8}

$\Rightarrow$ x +3 < 8 x $\in$W

$\Rightarrow$ x < 8 - 3

$\Rightarrow$ x < 5 and x $ϵ$ W

$\Rightarrow$ x = 0,1,2,3,4​​​​​​

$\Rightarrow$ M = {0, 1, 2, 3, 4}

So, elements of Set M are 0, 1, 2, 3 and 4.

N = {y : y = 2n -1, $n\in$ N and n < 5}

As, n < 5 , n$\in N$

$\Rightarrow$ n = 1, 2, 3 and 4

n = 1 $\Rightarrow$ y = 2(1) -1 =1
n = 2 $\Rightarrow$ y = 2(2) -1 =4 -1=3
n = 3 $\Rightarrow$ y = 2(3) -1 =6 -1=5
n = 4 $\Rightarrow$ y = 2(4) -1 =8- 1=7
$\Rightarrow$y = {1,3,5,7}

So, Elements of N are 1,3,5 and 7.
Therefore, elements of M and N are not identical.

Hence, sets M and N are not equal