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, ...

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Standard VIII

Mathematics

Singleton 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 ________.

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Solution

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

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

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

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

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

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

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

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

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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 ________.

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