State the following set is finite are infinite- x - 4 -2x - -6- x - ZIf it is finite then write 1 else write 0-

Given, #160; x : 4 2x gt; 6 , x ϵ Z ⇒ 4 2x gt; 6 ⇒ #160; 2x gt; 10 ⇒ #160;x lt; 5 So, values of x are ...

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Standard VII

Mathematics

Finite and Infinite Set

State the fol...

Question

State the following set is finite are infinite.
{ $x$ : $4 - 2 x > - 6$ , $x ϵ Z$ }
If it is finite then write $1$ else write $0$ .

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Solution

Given, { $x$ : $4 - 2 x > - 6$ , $x ϵ Z$ }
$\Rightarrow 4 - 2 x > - 6$
$\Rightarrow - 2 x > - 10$
$\Rightarrow x < 5$
So, values of $x$ are integer values less than $5$ .
Hence, elements of the set $4, 3, 2, 1, 0, - 1, - 2....$ . are infinite.

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State the following set is finite are infinite.{x : 4−2x>−6, xϵZ}If it is finite then write 1 else write 0.

Given, {x : 4−2x>−6, xϵZ}⇒4−2x>−6⇒−2x>−10⇒x<5So, values of x are integer values less than 5.Hence, elements of the set 4,3,2,1,0,−1,−2..... are infinite.

State the following set is finite are infinite.
{ $x$ : $4 - 2 x > - 6$ , $x ϵ Z$ }
If it is finite then write $1$ else write $0$ .

Given, { $x$ : $4 - 2 x > - 6$ , $x ϵ Z$ }
$\Rightarrow 4 - 2 x > - 6$
$\Rightarrow - 2 x > - 10$
$\Rightarrow x < 5$
So, values of $x$ are integer values less than $5$ .
Hence, elements of the set $4, 3, 2, 1, 0, - 1, - 2....$ . are infinite.