If U - x - x - N - A - x - x - 2n- n - N and B - x - x is a prime number- then A - B is a set with cardinality -

U = {x : x ∈ nbsp;N } ⇒ U = {1, 2, 3, 4, 5,...} A = {x : x = 2n, n ∈ nbsp;N } ⇒ A = {2, 4, 6, 8,...} B = {x : x is a prime number} ⇒ B = {2, 3, 5, 7, ...

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

Byju's Answer

Standard IX

Mathematics

Singleton Set and Empty Set

If U = x : x ...

Question

$If U = {x : x \in N},$ $A = {x : x = 2 n, n \in N}$ and $B = {x : x is a prime number},$ then $A \cap B$ is a set with cardinality ________.

infinity

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

one

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

two

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

zero

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

Open in App

Solution

The correct option is B
one

$U = {x : x \in N}$

$\Rightarrow U = {1, 2, 3, 4, 5, . . .}$

$A = {x : x = 2 n, n \in N}$

$\Rightarrow A = {2, 4, 6, 8, . . .}$

$B = {x : x is a prime number}$

$\Rightarrow B = {2, 3, 5, 7, 11, . . .}$

$\Rightarrow A \cap B = {2}$ as 2 is the only even prime number.

Hence, $A \cap B$ is a set with cardinality one.

Suggest Corrections

Similar questions

Q. Let

A = \{x : x \in N\}, B = \{x : x - 2 n, n \in N\}, C = \{x : x = 2 n - 1, n \in N\}

and D = {x : x is a prime natural number}. Find:
(i)

A \cap B

(ii)

A \cap C

(iii)

A \cap D

(iv)

B \cap C

(v)

B \cap D

(vi)

C \cap D

Let A = { $x : x ϵ N$ }, B = { $x : x = 2 n, n ϵ N$ }, C = { $x : x = 2 n - 1, n ϵ N$ } and , D = {x: x is a prime natural number}. Find :

(i) $A \cap B$ (ii) $A \cap C$

(iii) $A \cap D$ (iv) $B \cap C$

(v) $B \cap D$ (vi) $C \cap D$

Given the universal set = Universal ~set = ${x : x \in N a n d x < 20}$ ~find:

(i) A = ${x : x = 3 p; p \in N}$

(ii) B = ${y : y = 2 n + 3, n \in N}$

(iii) C = ${x : x i s d i v i s i b l e b y 4}$

$If U = {x : x \in N},$ $A = {x : x = 2 n, n \in N}$ and $B = {x : x is a prime number},$ then $A \cap B$ is a set with cardinality ________.

If A = {x : x = 2 n, n \in N}

and

B = {x : x is a prime number},

then

A and B

are ________ sets.

Join BYJU'S Learning Program

If U={x:x∈N}, A={x:x=2n,n∈N} and B={x:x is a prime number}, then A∩B is a set with cardinality ________.

The correct option is B one U={x:x∈N} ⇒U={1,2,3,4,5,...} A={x:x=2n,n∈N} ⇒A={2,4,6,8,...} B={x:x is a prime number} ⇒B={2,3,5,7,11,...} ⇒A∩B={2} as 2 is the only even prime number. Hence, A∩B is a set with cardinality one.

$If U = {x : x \in N},$ $A = {x : x = 2 n, n \in N}$ and $B = {x : x is a prime number},$ then $A \cap B$ is a set with cardinality ________.