2019 question paper
Discrete Mathematics
13 questions
Q1a. The statement p → q is logically equivalent to (i) p ∨ q (ii) p ∨ ~q (iii) ~p ∨ q (iv) ~p → q20192m
Module 3: Propositional Logic & Proof Techniques.
View this question on its own page →The statement p → q is logically equivalent to
(i) p ∨ q
(ii) p ∨ ~q
(iii) ~p ∨ q
(iv) ~p → qQ1b. The contrapositive of the conditional statement p \rightarrow q is (i) q \rightarrow p (ii) \sim p \rightarrow \sim q (iii) p \rightarrow q (iv) \sim q \rightarrow \sim p20192m
Module 3: Propositional Logic & Proof Techniques.
View this question on its own page →The contrapositive of the conditional statement is
(i)
(ii)
(iii)
(iv)Q1c. If A and B are two nonempty sets having n elements in common, then A \times B and B \times A will have how many elements in common? (i) 2^n (ii) n^2 (iii) n^4 (iv) 2n20192m
Module 1: Sets, Relation and Function.
View this question on its own page →If and are two nonempty sets having elements in common, then and will have how many elements in common?
(i)
(ii)
(iii)
(iv)Q1d. If a set A have n elements, then how many relations will be there on set A? (i) n^2 (ii) 2^(n^2) (iii) 2^n (iv) 2n20192m
Module 1: Sets, Relation and Function.
View this question on its own page →If a set A have n elements, then how many relations will be there on set A?
(i) n^2
(ii) 2^(n^2)
(iii) 2^n
(iv) 2nQ1e. (e) If P(Φ) represents the power set of Φ, then n(P(P(P(Φ)))) equal to (i) 1 (ii) 2 (iii) 3 (iv) 420192m
Module 1: Sets, Relation and Function.
View this question on its own page →(e) If P(Φ) represents the power set of Φ, then n(P(P(P(Φ)))) equal to
(i) 1
(ii) 2
(iii) 3
(iv) 4Q1f. (f) For the poset [{3, 5, 9, 15, 24, 45}]; divisor of | the bus of {3, 5} is (i) 3 (ii) 5 (iii) 15 (iv) 4520192m
Module 1: Sets, Relation and Function.
View this question on its own page →(f) For the poset [{3, 5, 9, 15, 24, 45}]; divisor of | the bus of {3, 5} is
(i) 3
(ii) 5
(iii) 15
(iv) 45Q1g. (g) If (S, *) is a monoid, where S = {1, 2, 3, 6} and * is defined by a * b = lcm(a, b), where a, b ∈ S, then the identity element is (i) 1 (ii) 2 (iii) 3 (iv) 620192m
Module 1: Sets, Relation and Function.
View this question on its own page →(g) If (S, *) is a monoid, where S = {1, 2, 3, 6} and * is defined by a * b = lcm(a, b), where a, b ∈ S, then the identity element is
(i) 1
(ii) 2
(iii) 3
(iv) 6Q1h. (h) The total number of subgroups of group G of prime order is (i) 1 (ii) 2 (iii) 3 (iv) 420192m
Module 1: Sets, Relation and Function.
View this question on its own page →(h) The total number of subgroups of group G of prime order is
(i) 1
(ii) 2
(iii) 3
(iv) 4Q1i. (i) The number of edges in a bipartite graph with n vertices is at most (i) n^2/2 (ii) n^2/4 (iii) n^2 (iv) 2n20192m
Module 1: Sets, Relation and Function.
View this question on its own page →(i) The number of edges in a bipartite graph with n vertices is at most (i) n^2/2 (ii) n^2/4 (iii) n^2 (iv) 2n
Q2a. Using truth table, show that- (i) ((p → (q → r)) → ((p → q) → (p → r))) is a tautology; (ii) ¬(q → r) ∧ r ∧ (p → q) is a contradiction.201914m
Module 3: Propositional Logic & Proof Techniques.
View this question on its own page →Using truth table, show that-
(i) ((p → (q → r)) → ((p → q) → (p → r))) is a tautology;
(ii) ¬(q → r) ∧ r ∧ (p → q) is a contradiction.Q2b. Obtain the principal disjunctive normal form (PDNF) and principal conjunctive normal form (PCNF) of the statement (p → (q ∧ r)) ∧ (¬p → (¬q ∧ ¬r)).201914m
Module 3: Propositional Logic & Proof Techniques.
View this question on its own page →Obtain the principal disjunctive normal form (PDNF) and principal conjunctive normal form (PCNF) of the statement
(p → (q ∧ r)) ∧ (¬p → (¬q ∧ ¬r)).Q3a. For any sets A and B, prove that (i) (A ∪ B)' = A' ∩ B' (ii) (A ∩ B)' = A' ∪ B'201914m
Module 1: Sets, Relation and Function.
View this question on its own page →For any sets A and B, prove that
(i) (A ∪ B)' = A' ∩ B'
(ii) (A ∩ B)' = A' ∪ B'Q3b. If two sets A and B have n elements in common, then show that the sets A × B and B × A will have 2^n elements in common.20197m
Module 1: Sets, Relation and Function.
View this question on its own page →If two sets A and B have n elements in common, then show that the sets A × B and B × A will have 2^n elements in common.