DISCRETE MATHEMATICS-1, Semester 1(2021-24), Feb 2022

 

SAINTGITS COLLEGE OF APPLIED SCIENCES

          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 = 4425.

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.    and .

      A V B =

      A B =

                                              

 

                                                                       

                                                (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 q) ‎ (pvq), if all the 

      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 ( ) = +2

          f ( ) = +2

          f ( ) = f ( )

             +2 = +2

         =

          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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