If A - y - x 2- y 2-1- x - N and B - y - x 2- y 2-4- x - N - then n A - B isA- 0B- 1C- 3D- infinite

The correct option is A 0A={y:x^2+y^21,x∈ℕ} We know that, y^2≥0, x^2≥1 ⇒ x^2 +y^2 ≥ 1 ⇒ A={ }=ϕ B={y:x^2+y^2=4, x∈ℕ} y^2≥0, x^2≥1 ⇒ B={ √(3),0,√(3)} ∴ n(A× B ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Algebra of Complex Numbers

If A = y : x ...

Question

If $A = {y : x^{2} + y^{2} < 1, x \in N}$ and $B = {y : x^{2} + y^{2} = 4, x \in N}$ , then $n (A \times B)$ is

0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

infinite

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $0$
$A = {y : x^{2} + y^{2} < 1, x \in N}$
We know that,
$y^{2} \geq 0, x^{2} \geq 1 \Rightarrow x^{2} + y^{2} \geq 1 \Rightarrow A = {} = ϕ$

$B = {y : x^{2} + y^{2} = 4, x \in N} y^{2} \geq 0, x^{2} \geq 1 \Rightarrow B = {- \sqrt{3}, 0, \sqrt{3}}$
$∴ n (A \times B) = 0$

Suggest Corrections

Similar questions

Q. If

A = {y : x^{2} + y^{2} < 1, x \in N}

and

B = {y : x^{2} + y^{2} = 4, x \in N},

then

n (A \times B)

Q. If

A = {(x, y) : x^{2} + y^{2} \leq 1; x, y ϵ R}

and

B = {(x, y) : x^{2} + y^{2} \geq 4; x, y ϵ R}

, then

Q. If

A = {(x, y) : x^{2} + y^{2} \leq 1 x, y \in R}

and

B = {(x, y) : x^{2} + y^{2} \leq 16 x, y \in R}

, then

Q. If

A = {(x, y) : x^{2} + y^{2} = 25}

and

B = {(x, y) : x^{2} + 9 y^{2} = 144}

; then

A \cap B

contains

If A = [(x,y): $x^{2} + y^{2} = 25$ ] And B = [(x,y): $x^{2} + 9 y^{2} = 144], t h e n A \cap B$ contains

Join BYJU'S Learning Program

If A={y:x2+y2<1,x∈N} and B={y:x2+y2=4,x∈N}, then n(A×B) is

The correct option is A 0A={y:x2+y2<1,x∈N} We know that, y2≥0, x2≥1⇒x2+y2≥1⇒A={ }=ϕ B={y:x2+y2=4,x∈N}y2≥0, x2≥1⇒B={−√3,0,√3} ∴n(A×B)=0

If $A = {y : x^{2} + y^{2} < 1, x \in N}$ and $B = {y : x^{2} + y^{2} = 4, x \in N}$ , then $n (A \times B)$ is