If A - x - x 2-5 x -6-0 and B - y - y - Z - 3- y -2- - 5- then the number of relations from A to B is

A={x:x^2 5x+6=0} ⇒ x^2 5x+6=0 ⇒ (x 2)(x 3)=0 ⇒ x=2,3 ⇒ A={2,3} B={y:y∈ℤ,3|y 2|≤5} 3|y 2|≤5 Case :1 When y≥2 ⇒3 y 2≤5 ⇒5 y≤7 Case :2 When y lt;2 ⇒3 2 y≤5 ⇒1 ...

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Byju's Answer

Standard XI

Mathematics

Inequality

If A = x : x ...

Question

If $A = {x : x^{2} - 5 x + 6 = 0}$ and $B = {y : y \in Z, 3 < | y - 2 | \leq 5}$ , then the number of relations from $A$ to $B$ is

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Solution

$A = {x : x^{2} - 5 x + 6 = 0}$
$\Rightarrow x^{2} - 5 x + 6 = 0$
$\Rightarrow (x - 2) (x - 3) = 0$
$\Rightarrow x = 2, 3$
$\Rightarrow A = {2, 3}$

$B = {y : y \in Z, 3 < | y - 2 | \leq 5}$
$3 < | y - 2 | \leq 5$
Case $: 1$ When $y \geq 2$
$\Rightarrow 3 < y - 2 \leq 5$
$\Rightarrow 5 < y \leq 7$

Case $: 2$ When $y < 2$
$\Rightarrow 3 < 2 - y \leq 5$
$\Rightarrow 1 < - y \leq 3$
$\Rightarrow - 3 \leq y < - 1$

Since, $y \in Z$
$y = {- 3, - 2, 6, 7}$
$B = {- 3, - 2, 6, 7}$

Number of relations from $A$ to $B$ $= 2^{n (A) \cdot n (B)} = 2^{2 \cdot 4} = 256$

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Q. If

A = {x : x^{2} - 5 x + 6 = 0}

and

B = {y : y \in Z, 3 < | y - 2 | \leq 5},

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A = {x : x^{2} - 5 x + 6 = 0}

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then prove that

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If A={x:x2−5x+6=0} and B={y:y∈Z,3<|y−2|≤5}, then the number of relations from A to B is

If $A = {x : x^{2} - 5 x + 6 = 0}$ and $B = {y : y \in Z, 3 < | y - 2 | \leq 5}$ , then the number of relations from $A$ to $B$ is