
Prove the following:
and , where is the universal set

Important Questions on Sets
Prove the following:
for all

Prove that and .

Prove that

If and are two sets such that has objects, has objects and has objects; how many objects does have ?

In a group of people, can speak Hindi and can speak English. How many people can speak both Hindi and English ?

In a group of people, like coffee, like tea and each person in the group likes at least one of the two drinks. people like both tea and coffee, how many people are in the group?

In a class of students, each student likes to play either cricket or hockey. students like to play cricket and students like to play both the games; how many students play hockey?

In a class of students, were listed as taking apple juice, as taking orange juice and were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice?
