**MA8351 DM Question Papers**

Anna University Regulation 2017 CSE **MA8351 DM Question Papers for previous years** are provided below. **Previous Year Question Papers for **CSE **3rd SEM MA8351 Discrete Mathematics, Engineering** are listed down for students to make perfect utilization and score maximum marks with our study materials.

### Anna University Regulation 2017 (CSE) 3rd SEM MA8351 DM – Discrete Mathematics question paper

1. Construct the truth table for the compound proposition (𝑝→𝑞)↔(¬𝑝→¬𝑞).

2.Construct the truth table for the compound proposition (𝑝→𝑞)→(𝑞→𝑝).

3.What are the contra positive, the converse and the inverse of the conditional statement “If you work hard then you will be rewarded”.

4.Find the truth table for the statement 𝑝→¬𝑞.

5.Give the truth value of 𝑇 ↔ 𝑇 ⋀ 𝐹.

6.Write the symbolic representation and give its contra positive statement of “If it rains today, then I buy an umbrella” .

7.When do you say that two compound propositions are equivalent ?

8.Show that ( 𝑝→𝑟)∧(𝑞→𝑟)𝑎𝑛𝑑 (𝑝∨𝑞)→𝑟 are logically equivalent.

9.Show that the propositions 𝑝→𝑞 𝑎𝑛𝑑 ¬𝑝∨𝑞 are logically equivalent.

10.Without using truth table show that 𝑝→(𝑞→𝑝)⟺¬𝑝→(𝑝→𝑞).

11.Show that (𝑝→(𝑞→𝑟))→((𝑝→𝑞)→(𝑝→𝑟)) is a tautology.

12.Is ¬𝑝∧(𝑝∨𝑞))→𝑞 a tautology?

13.Using the truth table, show that the proposition 𝑝∨¬(𝑝∧𝑞) is a tautology.

14.Given 𝑃= {2,3,4,5,6}, state the truth value of the statement (∃𝑥∈𝑝)(𝑥+3=10 ).

15. Let 𝐸={−1,0,1,2} denote the universe of discourse. If 𝑃(𝑥,𝑦)=𝑥+𝑦+1, find the truth value of (∀𝑥)(∃𝑦)𝑃(𝑥,𝑦).

16.Find a counter example, if possible, to these universally quantified statements, Whose the universe of discourse for all variables consists of all integers. (a) ∀𝑥∀𝑦 (𝑥2 =𝑦2→𝑥=𝑦). (b) ∀𝑥∀𝑦 (𝑥𝑦≥𝑥).

17.What are the negations of the statements ∀𝑥 (𝑥2>𝑥) 𝑎𝑛𝑑 ∃𝑥 (𝑥2=2)?

18.Write the negation of the statement(∃𝑥)(∀𝑦)𝑃(𝑥,𝑦).

19.Give an indirect proof of the theorem “ If 3𝑛+2 is odd, then n is odd

20.Prove that 𝑝,𝑝→𝑞,𝑞→𝑟 ⟹𝑟

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