List all the elements of each of the sets given below

Question:

 List all the elements of each of the sets given below

$H=\{x: x \in Z,|x| \leq 2\}$

 

Solution:

Given $x \in Z$ and $|x| \leq 2$

Z is a set of integers

Integers are …-3, -2 , -1, 0, 1, 2, 3, …

Now, if we take x = -3 then we have to check that it satisfies the given condition |x| ≤ 2

$|-3|=3>2$

So, $-3 \notin H$

If $x=-2$ then $|-2|=2[$ satisfying $|x| \leq 2]$

So, $-2 \in H$

If $x=-1$ then $|-1|=1[$ satisfying $|x| \leq 2]$

$\therefore-1 \in H$

If $x=0$ then $|0|=0$ [satisfying $|x| \leq 2$ ]

$\therefore 0 \in H$

If $x=1$ then $|1|=1$ [satisfying $|x| \leq 2$ ]

$\Rightarrow 1 \in H$

If $x=2$ then $|2|=2$ [satisfying $|x| \leq 2$ ]

So, $2 \in H$

If $x=3$ then $|3|=3>2$ [satisfying $|x| \leq 2$ ]

So, $3 \notin \mathrm{H}$

So, $H=\{-2,-1,0,1,2\}$

So, $E=\{0,1\}$

 

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