If A - x - x - Z- and - x 2-5 x -6-6-5 x - x 2- then cardinality of set A is

|x^2+5x 6|=6 5x x^2 Let x^2+5x 6 = t, then nbsp; ⇒ |t| = t ⇒ t ≤ 0 ⇒ x^2+5x 6≤ 0 ⇒ (x+6)(x 1)≤ 0 ⇒ 6≤ x≤ 1 ∴ x∈ [ 6,1] Since, x∈ℤ ⇒ x ∈{ 6, 5, 4, 3, 2, 1,0, ...

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Standard XII

Mathematics

Cardinality of Sets

If A = x , x ...

Question

If $A = {x, x \in Z and | x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}}$ , then cardinality of set $A$ is

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Solution

$| x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}$
Let $x^{2} + 5 x - 6 = t$ , then
$\Rightarrow | t | = - t \Rightarrow t \leq 0$
$\Rightarrow x^{2} + 5 x - 6 \leq 0$
$\Rightarrow (x + 6) (x - 1) \leq 0$
$\Rightarrow - 6 \leq x \leq 1$
$∴ x \in [- 6, 1]$
Since, $x \in Z$
$\Rightarrow x \in {- 6, - 5, - 4, - 3, - 2, - 1, 0, 1}$
$∴ n (A) = 8$

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Cardinality of Sets

Standard XII Mathematics

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If A={x,x∈Z and |x2+5x−6|=6−5x−x2}, then cardinality of set A is

|x2+5x−6|=6−5x−x2 Let x2+5x−6=t, then ⇒|t|=−t⇒t≤0 ⇒x2+5x−6≤0 ⇒(x+6)(x−1)≤0 ⇒−6≤x≤1 ∴x∈[−6,1] Since, x∈Z ⇒x∈{−6,−5,−4,−3,−2,−1,0,1} ∴n(A)=8

If $A = {x, x \in Z and | x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}}$ , then cardinality of set $A$ is