# Which of the following are pairs of equal sets?

Question:

Which of the following are pairs of equal sets?

$E=\left\{x: x \in Z, x^{2} \leq 4\right\}$ and $F=\left\{x: x \in Z, x^{2}=4\right\}$

Solution:

Equal Sets = Two sets A and B are said to be equal if they have exactly the

same elements & we write A = B

We have

$E=\left\{x: x \in Z, x^{2} \leq 4\right\}$

Here, $x \in Z$ and $x^{2} \leq 4$

If $x=-2$, then $x^{2}=(-2)^{2}=4=4$

If $x=-1$, then $x^{2}=(-1)^{2}=1<4$

If $x=0$, then $x^{2}=(0)^{2}=0<4$

If $x=1$, then $x^{2}=(1)^{2}=1<4$

If $x=2$, then $x^{2}=(2)^{2}=4=4$

So,

$E=\{-2,-1,0,1,2\}$

and $F=\left\{x: x \in Z, x^{2}=4\right\}$

Here, $x \in Z$ and $x^{2}=4$

If $x=-2$, then $x^{2}=(-2)^{2}=4=4$

If $x=2$, then $x^{2}=(2)^{2}=4=4$

So, $F=\{-2,2\}$

∴ E ≠ F because the elements in the both the sets are not equal.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}