Question

in a group of 50 people, 35 speaks Hindi, 25 speak both English and Hindi and all the people speak at least one of the language. how many people speak only English and not Hindi? how many people speak English?

Answer 1

AuB >> A union B
AiB >> A intersection B

sol. Let A --- Hindi speaking and B--- English speaking
we have total no. of people to be 50 and all of them speak atleast one language so
Universal set = AuB
now n(A) = 35
n(AiB) = 25
now we know that
n(AuB) = n(A) + n(B) - n(AiB)
so 50 = 35 +n(B) - 25
so n(B) = 50-10 =40 ...
now n(English only) = 40 - 25 = 15...

Answer 2

Hey!

AuB >> A union B

AiB >> A intersection B

sol. Let A -Hindi speaking and B-English speaking

we have total no. of people to be 50 and all of them speak atleast one language so

Universal set = AuB

now n(A) = 35

n(AiB) = 25

now we know that

n(AuB) = n(A) + n(B) - n(AiB)

so 50 = 35 +n(B) - 25

so n(B) = 50-10 =40

now n(English only) = 40 - 25 = 15