DISCRETE MATHEMATICS-1, Semester 1(2021-24), Feb 2022
PATHAMUTTOM, KOTTAYAM
Model
Examination, FEB 2022
PG
Department of Computer Applications & Artificial Intelligence
First
Semester
DISCRETE MATHEMATICS-1
Total : 80 marks Time: 3 hours
Answer Key
Section A
Answer any 6 questions. Each question carries 3 marks.
(Write in not less than a paragraph)
1. “Today is not Sunday”. Draw the truth table of negation.
2. Draw the truth table for:
a) Conditional
statement (Refer text)
b) Biconditional
statement (Refer text)
3. “If it is sunny today then we will go to the park”.
4. Define the following rules of inferences:
a) Modus
ponens (Refer text)
b) Hypothetical
syllogism (Refer text)
5. Power set of the set {0, 1, 2} = { {}, {0}, {1}, {2}, {0,1}, {1,2},
{0,2}, {0,1,2} }
6. The value of
7. Draw the Venn-diagram.
8. Lcm (120,500) = 3000 and gcd (120,500) = 20
9. To show that 101 is prime, use theorem 2 of Module 3.
10. State the theorem.
11. Define equivalence relation with an example. Also give any example
for transitive
relation.
12.
A V B =
A
(6 x 3 = 18 Marks)
Section B
Answer any 4 questions. Each question carries 8 marks.
(Write in not less than 2 pages)
13. Define tautology and contradiction. Draw the truth table for (p
output is true then it is a tautology.
14. Draw the truth table for
the De Morgan laws (Refer text).
15. p: you send me an e-mail
message
q: I will finish writing
the program
r: I will go to sleep
early
s: I will wake up feeling
refreshed
For complete solution
refer text.
16. Refer text.
17. (a) f (
f (
f (
Hence it is a one-one
function.
(b) Let f and g be the
functions from the set of integers to the set of integers defined by
f(x)= 2x+3 and g(x) = 3x+2. What is the
composition of f and g? What is the
composition of g and
f?
18. Refer text.
19. 1=14.110 - 19.81
20. Refer text.
21. Define total ordering and
totally ordered set with example.
(4 x 8 = 32 Marks)
Section C
Answer up to 3 questions carrying 15 marks each. However, total marks
for this section should not exceed 30 marks. Marks scored over 30 will be
ignored
22. Refer text.
23. Refer text.
24. Refer text.
25. (a) Given that a R b if and only if a = b or a=
-b then, prove that R is reflexive,
symmetric
and transitive relation.
(b) Refer text.
(Maximum 30 Marks)
[Scan QR code for Answer Key]
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