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 ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

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}

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

A \cup B = B \cup A

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

A \cap B = B \cap A

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

A \subset B

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

Open in App

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 $A \subset̸ B .$

Suggest Corrections

Similar questions

Q. 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.

Q. Let

a, b \in N

with

2 \leq a \leq 2020

and

2 \leq b \leq 2020

P, Q, R

are three sets defined as

P = {(a, b) : {log}_{a} b + 6 {log}_{b} a = 5}

Q = {(a, b) : b = a^{2}}

R = {(a, b) : b = a^{3}} .

Then which of the following is (are) correct?

Q. Consider the following statements :

1. N \cup (B \cap Z) = (N \cup B) \cap Z

for any subset

B

R,

where

N

is the set of positive integers,

Z

is the set of integers,

R

is the set of real numbers.

2.

Let

A = {n \in N : 1 \leq n \leq 24, n is a multiple of 3} .

There exists no subset

B

N

such that the number of elements in

A

is equal to the number of elements in

B .

Which of the above statements is/are correct?

Q. Two sets:

X, Y

such that

X = {x : x \in N; x^{2} - 5 x + 6 = 0} &

B = {1, 2, 5, 3},

then

A \cap B =

Q. Two sets such that

n (B - A) = 25; n (A - B) = 15

and

n (A \cap B) = 10,

then

n (A \cup B) =

Join BYJU'S Learning Program

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.