Write true (T) or false (F):

(i) The number of proper subsets of a set containing n elements is 2ⁿ.

(ii) Any set A and its complement are equivalent sets.

(iii) The complement of a set is a subset of U.

(iv) If n(A ∩ B) = Φ, then n(B - A) = n(B)

(v) If two sets A and B are disjoint, then n(A ∪ B) = n(A) + n(B)

Sid is given a few sets. These are represented as A, B, C, D, E, F and G on a plain sheet of paper as a Venn Diagram.

(1) How many empty sets are there in the given Venn Diagram ?

1. 3
2. 2
3. 1
4. 0

(2) How many singleton sets are there in the given Venn Diagram ?

1. 0
2. 1
3. 2
4. 3

(3) How many pairs of equivalent sets are there in the given Venn Diagram ?

1. 1
2. 2
3. 3
4. 4

(4) How many pairs of equal sets are there in the given Venn Diagram ?

1. 0
2. 1
3. 2
4. 3

In a class there are 27 students. Out of these 14 study Psychology and 19 study Geography. There are 11 students who study both Psychology and Geography.

(1) How many students study Psychology but not Geography ?

1. 3
2. 4
3. 5
4. 6

(2) How many students study Geography but not Psychology ?

1. 7
2. 8
3. 9
4. 11

(3) How many students study neither Psychology nor Geography ?

1. 8
2. 7
3. 6
4. 5

(4) What is the difference between the number of students who study Psychology only and those who study Geography only ?

1. 4
2. 5
3. 6
4. 7

Assertion: Let P = {x : x is a factor of 24} and Q = {x : x is a factor of 30}.
P ∩ Q = {1, 2, 3, 6}.

Reason: The intersection of two sets A and B is the set of all those elements of A which are not in B.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.