If R is relation from A to B- where R-x-y-x-y-x2-y2-4- then the least value of nA- B is

R={(x,y):x,y∈ℤ,x^2+y^2≤4} From here x^2≥0, y^2≥0 Now 0≤ x^2≤4, 0≤ y^2≤ 4, x,y∈ℤ 2≤ x≤2, 2≤ y≤ 2,x,y∈ℤ ∴ A=B and the smallest set A can be { 2, 1,0,1,2} So n(A ...

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Standard XI

Mathematics

Number of Elements in a Cartesian Product

If R is relat...

Question

If $R$ is relation from $A$ to $B$ , where $R = {(x, y) : x, y \in Z, x^{2} + y^{2} \leq 4}$ , then the least value of $n (A \times B)$ is

25

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16

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9

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Solution

The correct option is A $25$
$R = {(x, y) : x, y \in Z, x^{2} + y^{2} \leq 4}$
From here $x^{2} \geq 0, y^{2} \geq 0$
Now $0 \leq x^{2} \leq 4, 0 \leq y^{2} \leq 4, x, y \in Z$
$- 2 \leq x \leq 2, - 2 \leq y \leq 2, x, y \in Z$
$∴$ $A = B$
and the smallest set $A$ can be ${- 2, - 1, 0, 1, 2}$
So $n (A \times B) = 25$

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If R is relation from A to B, where R={(x,y):x,y∈Z,x2+y2≤4}, then the least value of n(A×B) is

The correct option is A 25R={(x,y):x,y∈Z,x2+y2≤4} From here x2≥0,y2≥0 Now 0≤x2≤4,0≤y2≤4,x,y∈Z −2≤x≤2,−2≤y≤2,x,y∈Z ∴ A=B and the smallest set A can be {−2,−1,0,1,2} So n(A×B)=25

If $R$ is relation from $A$ to $B$ , where $R = {(x, y) : x, y \in Z, x^{2} + y^{2} \leq 4}$ , then the least value of $n (A \times B)$ is