2019 question paper

Discrete Mathematics

13 questions

1. 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.

   The statement p → q is logically equivalent to
   (i) p ∨ q
   (ii) p ∨ ~q
   (iii) ~p ∨ q
   (iv) ~p → q

   View this question on its own page →

   CopySearch GoogleAsk AI
2. Q1b. 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.

   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) $\sim q \rightarrow \sim p$

   View this question on its own page →

   CopySearch GoogleAsk AI
3. 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.

   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) $2n$

   View this question on its own page →

   CopySearch GoogleAsk AI
4. 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.

   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) 2n

   View this question on its own page →

   CopySearch GoogleAsk AI
5. Q1e. (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.

   (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) 4

   View this question on its own page →

   CopySearch GoogleAsk AI
6. Q1f. (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.

   (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) 45

   View this question on its own page →

   CopySearch GoogleAsk AI
7. Q1g. (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.

   (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) 6

   View this question on its own page →

   CopySearch GoogleAsk AI
8. Q1h. (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.

   (h) The total number of subgroups of group G of prime order is
   (i) 1
   (ii) 2
   (iii) 3
   (iv) 4

   View this question on its own page →

   CopySearch GoogleAsk AI
9. Q1i. (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.

   (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

   View this question on its own page →

   CopySearch GoogleAsk AI
10. 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.

    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.

    View this question on its own page →

    CopySearch GoogleAsk AI
11. Budget App•POCKETLY

    Pocketly on Android

    Log daily food, travel, and hostel expenses instantly. Set monthly spending limits and see where your money goes without complex spreadsheets.

    Install Pocketly
12. 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.

    Obtain the principal disjunctive normal form (PDNF) and principal conjunctive normal form (PCNF) of the statement
    (p → (q ∧ r)) ∧ (¬p → (¬q ∧ ¬r)).

    View this question on its own page →

    CopySearch GoogleAsk AI
13. 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.

    For any sets A and B, prove that
    (i) (A ∪ B)' = A' ∩ B'
    (ii) (A ∩ B)' = A' ∪ B'

    View this question on its own page →

    CopySearch GoogleAsk AI
14. 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.

    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.

    View this question on its own page →

    CopySearch GoogleAsk AI