Discrete Mathematics (MTH202)

1. The conjunction p ∧ q is True when _________.

   1. p is True, q is False
   2. p is False, q is True
   3. p is True, q is True
   4. p is False, q is False

2. The disjunction of p and q is written as ________.

   1. p ∨ q
   2. p ∧ q
   3. p XOR q
   4. None of the given

3. The logical statement p ∧ q means ________.

   1. p OR q
   2. p NOT q
   3. p AND q
   4. p XOR q

4. The disjunction p ∨ q is False when ________.

   1. p is False, q is True.
   2. p is True, q is False.
   3. p is True, q is True.
   4. p is False, q is False.

5. If p = It is raining, q = She will go to college
   "It is raining and she will not go to college”
   will be denoted by

   1. p ∧ ∼q
   2. p ∧ q
   3. ∼(p ∧ q)
   4. ∼p ∧ q

6. The negation of “Today is Friday” is

   1. Today is Saturday
   2. Today is not Friday
   3. Today is Thursday
   4. None of the given

7. ( p ∨ ∼p ) is the ________.

   1. Contradiction
   2. Conjunction
   3. Tautology
   4. Contingency

8. The converse of the conditional statement p → q is

   1. q → p
   2. ∼q → ∼p
   3. ∼p → ∼q
   4. None of the given

9. Let p be True and q be True, then ( ∼p ∧ q ) is ________.

   1. t ( where t is tautology. )
   2. c ( where c is contradiction. )
   3. True
   4. False

10. The contrapositive of the conditional statement 'If it is Sunday, then I go for shopping' is ________.

    1. I do Not go for shopping, then it is Not Sunday.
    2. I go for shopping, then it is Sunday.
    3. I do Not go for shopping, then it is Sunday.
    4. I go for shopping, then it is Not Sunday.

11. The statement p → q is logically equivalent to ∼q → ∼p

    1. True
    2. False

12. Let p → q be a conditional statement, then the statement q → p is called ________.

    1. Inverse
    2. Converse
    3. Contrapositive
    4. Double conditional

13. If p is false and q is false, then ∼p implies q is ________.

    1. True
    2. False

14. The converse of the conditional statement 'If I live in Quetta, then I live in Pakistan' is ________.

    1. If I live in Pakistan, then I live in Quetta.
    2. If I live in Pakistan, then I do Not live in Quetta.
    3. If I do Not live in Quetta, then I do Not live in Pakistan
    4. If I do Not live in Quetta, then I live in Pakistan

15. ∼(P → q) is logically equivalent to _________.

    1. p ∧ ∼q
    2. p ∨ ∼q
    3. ∼p ∧ q
    4. ∼p ∨ q

16. If p ↔ q is True, then ________.

    1. Only p is True.
    2. Only q is True.
    3. p and q both are True.
    4. None of the given.

17. 'p is equivalent to q' means ________.

    1. p is not necessary but p is sufficient for q.
    2. p is neither necessary nor sufficient for q.
    3. p is necessary and sufficient for q.
    4. p is necessary but not sufficient for q.

18. What is the truth value of the sentence?
    'It rains if and only if there are clouds.'

    1. True
    2. False

19. If p is false and q is true, then ∼p ↔ q is ________.

    1. True
    2. False

20. Let p1, p2, p3 be True premises in a given Truth Table. If the conjunctions of the Conclusion with each of p1, p2, p3 are True, then the argument is ________.

    1. False
    2. True
    3. Invalid
    4. Valid

21. The switches in parallel act just like ________.

    1. NOT gate
    2. AND gate
    3. OR gate
    4. XOR gate

22. Let A = {2, 3, 5, 7}, B = {2, 3, 5, 7, 2}, C = Set of first five prime numbers. Then from the following which statement is true ?

    1. A = B
    2. A = C
    3. B = C
    4. All the three sets are equal.

23. If A = Set of students of virtual university then A has been written in the _________.

    1. Tabular form
    2. Set builder form
    3. Descriptive form
    4. A is not a set

24. If A and B are any two sets, then A − B = B − A

    1. True
    2. False

25. x belongs to A or x belongs to B, therefore x belongs to ________.

    1. A intersection B
    2. A union B
    3. A difference B
    4. A symmetric difference B

26. Range of the relation {(0,1), (3,22), (90,34)} is __________ .

    1. {0, 3, 90}
    2. {1, 22, 34}
    3. {0, 1, 3}
    4. {0, 1, 3, 22, 90, 34}

27. Which of the followings is the product set A * B * C ? where A = {a}, B = {b}, and C = {c, d}.

    1. {(a, b, c), (a, b, d)}
    2. {(a, c, b), (a, d, b)}
    3. {(b, c, a), (b, d, a)}
    4. {(c, b, a), (d, b, a)}

28. Determine values of x and y, where (2x, x + y) = (8, 6).

    1. x = 3 and y = 5
    2. x = 4 and y = 2
    3. x = 6 and y = 12
    4. x = 4 and y = 12

29. Let R be the universal relation on a set A then which one of the following statement about R is true?

    1. R is not symmetric
    2. R is not reflexive
    3. R is not transitive
    4. R is reflexive, symmetric and transitive.

30. Let R be a relation on a set A. If R is symmetric then its compliment is __________.

    1. Reflexive
    2. Irreflexive
    3. Symmetric
    4. Antisymmetric

31. Let R be a relation on a set A. If R is reflexive then its compliment is ____________.

    1. Reflexive
    2. Irreflexive
    3. Symmetric
    4. Antisymmetric

32. R = {(a,1), (b,2), (c,3), (d,4)} then the inverse of this relation is _______.

    1. {(a,1), (b,2), (3,c), (4,d)}
    2. {(1,a), (2,b), (3,c), (4,d)}
    3. {(a,1), (2,b), (3,c), (4,d)}
    4. {(1,a), (b,2), (3,c), (4,d)}

33. Let R be a relation on a set A. If R is reflexive then its compliment is ________ .

    1. Reflexive
    2. Irreflexive
    3. Symmetric
    4. Antisymmetric

34. Which relations below are functions?
    R1 = {(3,4), (4,5), (6,7), (8,9)}
    R2 = {(3,4), (4,5), (6,7), (3,9)}
    R3 = {(-3,4), (4,-5), (0,0), (8,9)}
    R4 = {(8,11), (34,5), (6,17), (8,19)}

    1. R1 and R3 are functions
    2. R1 and R2 are functions
    3. R2 and R4 are functions
    4. R3 and R2 are functions

35. For the following relation to be a function, x can not be what values?
    R = {(2,4), (x,1), (4,2), (5,6)}

    1. x cannot be 2, 4 or 5
    2. x cannot be 4, 1 or 6
    3. x cannot be 2, 4 or 6
    4. x cannot be 1, 2 or 6

36. Let X = {2, 4, 5} and Y= {1, 2, 4} and R be a relation from X to Y defined by R = {(2,4), (4,1), (a,2)}. For what value of ‘a‘ the relation R is a function ?

    1. 1
    2. 2
    3. 4
    4. 5

37. Let A = {1, 2, 3} and B = {2, 4} then number of functions from A to B are _________.

    1. 6
    2. 8
    3. 16
    4. 64

38. Let A = {1, 2, 3, 4} and B = {7} then the constant function from A to B is _________ .

    1. Onto
    2. One to one
    3. Both one to one and onto
    4. Neither one to one nor onto

39. One-to-One correspondence means the condition of ______.

    1. one-One
    2. identity
    3. onto
    4. one-One and onto

40. If a function (g o f)(x):X→Z is defined as (g o f)(x) = g(f(x)) for all x ∈ X. Then the function ________ is known as composition of f and g.

    1. (f o g)
    2. f^-1(g(x))
    3. (g o f)
    4. g^-1(f(x))

41. Let g be a function defined by g(x) = x + 1. Then the composition of (g o g)(x)is ______.

    1. x
    2. x + 1
    3. x + 2
    4. x² + 2x + 1

42. The functions 'f' and 'g' are inverse of each other if and only if their composition gives _______.

    1. constant function
    2. identity function
    3. bijective function
    4. injective function

43. The functions f o g and g o f are always equal.

    1. TRUE
    2. FALSE

44. A set is called finite, if and only if, it is the ________ or there is ________ .

    1. empty set, onto
    2. empty set, one-to-one
    3. one-to-one, onto
    4. empty set, bijective

45. If f and g are two one-to-one functions, then their composition that is gof is one-to-one.

    1. TRUE
    2. FALSE

46. Let f(x) = x² + 1 define functions f from R to R and c = 2 be any scalar, then c.f(x) is ______.

    1. 2
    2. x² + 1
    3. 2x² - 1
    4. 2x² + 2

47. The set Z of all integers is _____.

    1. uncountable
    2. countable

48. Let f(x) = 3x and g(x) = x + 2 define functions f and g from R to R, then (f.g)(x) is _____.

    1. 2x − 2
    2. 3x + 2
    3. 4x + 2
    4. 3x² + 6x

49. Real valued function is a function that assigns _______ to each member of its domain.

    1. negative real number
    2. positive real number
    3. only a real number
    4. any arbitrary real number

50. Let f(x)=3x and g(x) = 3x − 2 define functions f and g from R to R. Then (f+g)(x) = ________.

    1. −2
    2. 6x + 2
    3. 6x − 2
    4. 6x.x − 2

51. The total number of terms in an arithmetic series 0 + 5 + 10 + 15 + .... + 50 are ________.

    1. 9
    2. 10
    3. 11
    4. infinite

Select a course code for Objective Questions:

ACC311 ACC501 BIF101 BIF401 BIF501 BIO101 BIO201 BIO202 BIO203 BIO204 BIO301 BIO302 BIO303 BIO401 BIO503 BNK603 BT101 BT201 BT301 BT302 BT401 BT402 BT403 BT404 BT405 BT406 BT501 BT504 BT505 BT604 CHE201 CHE301 CS001 CS101 CS201 CS202 CS204 CS301 CS302 CS304 CS311 CS401 CS402 CS403 CS408 CS501 CS502 CS504 CS506 CS508 CS601 CS602 CS604 CS605 CS607 CS609 CS610 CS614 CS707 CS710 ECO401 ECO402 ECO403 ECO404 EDU302 EDU401 EDU402 EDU501 EDU601 ENG101 ENG201 ENG301 ENG501 FIN611 FIN624 FIN625 ISL201 IT430 MCM101 MCM301 MGMT623 MGT101 MGT211 MGT301 MGT401 MGT402 MGT501 MGT502 MGT503 MGT510 MGT601 MGT603 MKT501 MKT610 MKT630 MTH101 MTH202 MTH302 MTH501 MTH601 MTH634 PAK301 PHY101 PHY301 PSY101 PSY403 PSY502 PSY512 SOC101 SOC301 SOC401 STA301 STA630 STA641 ZOO102 ZOO401 ZOO501 ZOO502 ZOO503 ZOO504 ZOO505 ZOO506 ZOO510 ZOO630

Select a course code for Subjective Questions:

ACC311 CS001 CS101 CS201 CS301 CS607 CS701 CS702 CS703 CS704 CS707 CS708 CS710 CS711 CS718 CS721 CS724 ECO401 ECO403 ENG101 ENG301 MGT703 MTH501 STA301