## MA8351 DM 2marks

Anna University Regulation 2017 IT MA8351 DM 2marks & 16marks for all 5 units are provided below. MA8351 DM Short answers, Question Bank for Discrete Mathematics Engineering are listed down for students to make perfect utilization and score maximum marks with our study materials.

MA8351 DISCRETE MATHEMATICS ENGINEERING QUESTION BANK UNIT-I 2-marks

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)?

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MA8351 DM 2marks

Anna University 3rd SEM IT DM 2marks 16 marks