Discrete Mathematics Answers

Prove that if A and B are any two sets such that A is proper subset of B, then A union B=B-
1) by direct method
2) by proving its contrapositive.
3) by contradiction.

In the context of admission to IGNOU, give example of the following-
1.an implication ,
2.the converse of (1) above.
3.a two way implication which is true.
4.a statement involving both for all and there exit.
5.the contrapositive of (1) above.

Which of the following statements are true? Give reasons for you answer. (This means that if you
think a statement is false, give a short proof or an example that shows it is false. If it is true, give a
short proof for saying so. For instance, to show that {1, Padma, blue} is a set’ is true, you need to
say that this is true because it is well defined collection of 3 objectives.)
(i){MTE-04, -3, Indira Gandhi} Is a set.
(ii) for any two sets A & B, A union of B complement = A intersection B.

Any subset of A × A is called a relation on the set A. A relation R on A is symmetric if
(a, b) ∈ R ⇒ (b, a) ∈ R ∀ a, b ∈ A. Give one example each, with justification, of
i) a symmetric relation on ,
ii) a relation that is not symmetric on the set {2, 3, 5, 7}.

Let U = {a,b,c,d,e,f,g}, X={a,c,e,g}, Y={a,b,c}, and Z={b,c,d,e,f}
1.2.1 Find Y n Z (3 Marks)
1.2.2 Find A U B (6 Marks)
1.2.3 Find X – Y (5 Marks)
1.2.4 Find X x Y

In a survey of a TriDelt chapter with 50 members, 19 were taking mathematics, 33 were taking English, and 7 were taking both. How many were not taking either of these subjects?

In the context of admission to IGNOU, give examples of the following:
i) an implication;
ii) the converse of (i) above;
iii) a two-way implication which is true;
iv) a statement involving both ∀ and ∃.
v) the contrapositive of (i) above.