If U - x - x - N - A - x - x -2 n - n - N and B - x - x is a prime number - then A - B is a set with cardinalityA- infinityB- zeroC- oneD- two

The correct option is C one 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 num ...

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Standard X

Mathematics

Cardinality of Sets

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

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zero

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one

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two

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Solution

The correct option is C
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.

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Similar questions

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

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)

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(ii)

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(iii)

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(iv)

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(v)

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(vi)

C \cap D

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and

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then

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are ________ sets.

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 ________.

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) $B \cap C$

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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 C 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 ________.