Q1 of 145 Page 47

If a set A and n elements then find the number of elements in its power set P(A).

The power set of set A is a collection of all subsets of A.


For example: if the set A is {1, 2} then all possible subsets of A would be {} (empty set), {1}, {2}, {1, 2}


Hence powerset of A that is P(A) will be {ϕ, {1}, {2}, {1,2}}


Now if the number of elements in set A is n then the number of elements in power set of A P(A) is 2n


More from this chapter

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14

In a town of 10,000 families, it was found that 40% of the families buy newspaper A, 20% buy newspaper B, 10% buy newspaper C, 5% buy A and B; 3% buy B and C, and 4% buy A and C. IF 2% buy all the three newspapers, find the number of families which buy

(i) A only,


(ii) B only,


(iii) none of A, B, and C.


 15

A class has 175 students. The following description gives the number of students one or more of the subjects in this class: mathematics 100, physics 70, chemistry 46, mathematics and physics 30; mathematics and chemistry 28; physics and chemistry 23; mathematics, physics and chemistry 18. Find

(i) how many students are enrolled in mathematics alone, physics alone and chemistry alone,


(ii) The number of students who have not offered any of these subjects.


 2

If A = ϕ then write P(A).

 3

If n(A) = 3 and n(B) = 5, find:

(i) The maximum number of elements in A ∪ B,


(ii) The minimum number of elements in A ∪ B.