Two sets given such that A-a-a is a prime number-25 -B-b-b- 10- b- 18- the select the correct statements-

Given two sets: A={a:a is a prime number lt;25} & B={b:b∈ℕ, 10≤ b≤ 18} Now, in roster form: A={2,3,5,7,11,13,17,19,23} & B={10,11,12,..., 16,17,18} No ...

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Byju's Answer

Standard XIII

Mathematics

Properties of Intersection of Sets

Two sets give...

Question

Two sets given such that $A = {a : a is a prime number < 25} &$
$B = {b : b \in N, 10 \leq b \leq 18},$ the select the correct statements.

A \cap B = {11, 13, 17}

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A \cup B = B \cup A

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A \cap B = B \cap A

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A \subset B

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Solution

The correct option is C $A \cap B = B \cap A$
Given two sets: $A = {a : a is a prime number < 25} &$
$B = {b : b \in N, 10 \leq b \leq 18}$
Now, in roster form:
$A = {2, 3, 5, 7, 11, 13, 17, 19, 23} &$
$B = {10, 11, 12, . . ., 16, 17, 18}$
Now, we know the commutative property of both union and intersection of sets.
$\Rightarrow A \cap B = B \cap A & A \cup B = B \cup A$
Also, $A \cap B = {11, 13, 17} .$
Also, this means $A \subset̸ B .$

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Two sets given such that A={a:a is a prime number<25} & B={b:b∈N,10≤b≤18}, the select the correct statements.

Two sets given such that $A = {a : a is a prime number < 25} &$
$B = {b : b \in N, 10 \leq b \leq 18},$ the select the correct statements.