Sets Set 4

is the set of all residents in a colony and is a relation defined on as follows:
"Two persons are related iff they speak the same language"
The relation  is

If is a set with 10 elements and , then the number of elements in is

Let and be a relation defined as "two elements of are related if they share exactly one letter". The relation is

The finite sets and have and elements respectively. if the total number of subsets of is 112 more than the total number of subsets of , then the volume of is

Let be a relation on a set Then, is

If then the number of elements in the set is

If is a multiple of and,
 is  a multiple of ; then  is

An investigator interviewed 100 students to determine the performance of three drinks milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and coffee, 30 students take coffee and tea, 25 students take mile and tea, 12 students take milk only, 5 students take coffee only and 8 students take tea only. Then, the number of students who did not take any of the three drinks, is

Consider the following statements:

Given , where is the universal set, and are subsets of , then equals to