# MA6566 Discrete Mathematics Important questions

## Sample MA6566 Discrete Mathematics Important questions:

3. Define a tautology. With an example.

A statement that is true for all possible values of its propositional variables is called
a tautology universely valid formula or a logical truth.
Example: p ∨ ￢q is a tautology.

4. When do you say that two compound statement proposition are equivalent.

Two compound proposition are said to be equivalent if then the have identical truth tables. (MA6566 Discrete Mathematics Important questions)

5. Give an indirect proof of the theorem if 3n+2 is odd, then n is odd.
Solution:

P: 3n+2 is odd
Q: n is odd
Hypothesis: Assume that ? → q is false.
Assume that ? ?? ???? ??? q is false.
i.e, n is not odd ⇒ n is even.
Analysis: If n is even then n=2k for some integer k.
3n+2= 3(2k)+2.
= 6k+2.
= 2(3k+1) (MA6566 Discrete Mathematics Important questions)

6. Define a universal specification.
(x)A(x) ⇒ ? ?

If a statement of the form (x)A(x) is assumed to be true , then the universal quantifier can be
dropped to obtain A(y) is true for any arbitrary object y in the universe.

7.Show that {∨,∧} is not functionally complete.

Solution: ¬? cannot be expressed using the connectives {∨,∧} .since no sets contribution of the
statement exists {∨,∧} as input if T and the output is F. (MA6566 Discrete Mathematics Important questions)

8. Write the converse, inverse, contra positive of „If you work hard then you will be rewarded‟
Solution:

p: you will be work hard.
q: you will be rewarded.
¬p: You will not be work hard.
¬ q: You will no tbe rewarded.
Converse: q→ p, If you will be rewarded then you will be work hard
Contrapositive: ¬ q→ p,if You will not be rewarded then You will not be work hard.
Inverse: ¬ p→ ¬ q, if You will not be work hard then You will no tbe rewarded.

(MA6566 Discrete Mathematics Important questions)

 Subject Name Discrete Mathematics Subject code MA6566 Regulation 2013

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