List all elements of following sers : C = { x:x is an integer {rm{; }}{x^2} le 4}

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1.Set Theory

easy

List all the elements of the following sers :

$C = \{ x:x$ is an integer ${\rm{; }}{x^2} \le 4\} $

Option A

Option B

Option C

Option D

Solution

$C = \{ x:x{\rm{ }}$ is an integer ${\rm{ }};{x^2} \le 4\} $

It can be seen that

${( – 1)^2} = 1\, \le \,4;{( – 2)^2} = 4\, \le \,4;{( – 3)^2} = 9\, > \,4$

$0^{2}=0 \leq 4$

$1^{2}=1 \leq 4$

$2^{2}=4 \leq 4$

$3^{2}=9>4$

$\therefore C=\{-2,-1,0,1,2\}$

Standard 11

Mathematics

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