Question

If A={x : x is a prime less than 20} and B = {x : x is whole number less than 10} then
verify n(A∪B) = n(A) + n(B) – n(A∩B).

Answer 1

Answer:

A = {2,3,5,7,11,13,17,19)

B = { 0,1,2,3,4,5,6,7,8,9,10}

AUB = { 0,1,2,3,4,5,6,7,8,9,10,1,13,17,19}

AnB = {2,3,5,7}

Now,

n(AUB) = n(A) + n(B) - n(AnB)

15 = 8 + 11 - 4

15 = 19 - 4

15 = 15

LHS = RHS

Hence verified

pls make it brainliest answer.

Answer 2

Concept

Any natural number higher than one that is not the sum of two smaller natural numbers is referred to be a prime number.

All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers that don't have decimals, fractions, or the negative sign.

Given

A={$x:x$ is a prime number less than $20$} and B = {$x:x$ is a whole number less than $10$}

Find

We have to find whether A and B satisfies the equation n(A∪B) = n(A) + n(B) – n(A∩B).

Solution

The prime numbers which are less than $20$ are-

2,3,5,7,11,13,17,19

Therefore, A is given as-

A={2,3,5,7,11,13,17,19}

So, n(A)=8

The whole numbers which are less than $20$ are-

0,1,2,3,4,5,6,7,8,9,10

Therefore, B is given as-

B={0,1,2,3,4,5,6,7,8,9,10}

So, n(B)=11

Now, (A∪B) is given as-

= {2,3,5,7,11,13,17,19}∪{0,1,2,3,4,5,6,7,8,9,10}

={0,1,2,3,4,5,6,7,8,9,10,11,13,17,19}

So, n(A∪B)=15

Also, (A∩B) is given as-

={2,3,5,7}

So, n(A∩B)=4

Substituting these values in the equation, n(A∪B) = n(A) + n(B) – n(A∩B), we get

15=8+11-4

15=19-4

15=15

Since, both the sides are equal.

Hence, A and B satisfies the equation n(A∪B) = n(A) + n(B) – n(A∩B).

#SPJ2