MCQOPTIONS
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MCQOPTIONS
This section includes 107 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Determine the truth value of statement ∃n (4n = 3n) if the domain consists of all integers. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 52. |
p ∨ q is logically equivalent to ________ |
| A. | ¬q → ¬p |
| B. | q → p |
| C. | ¬p → ¬q |
| D. | ¬p → q |
| Answer» E. | |
| 53. |
Let Q(x) be the statement “x < 5.” What is the truth value of the quantification ∀xQ(x), having domains as real numbers. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 54. |
p → q is logically equivalent to ________ |
| A. | ¬p ∨ ¬q |
| B. | p ∨ ¬q |
| C. | ¬p ∨ q |
| D. | ¬p ∧ q |
| Answer» D. ¬p ∧ q | |
| 55. |
p ∧ q is logically equivalent to ________ |
| A. | ¬ (p → ¬q) |
| B. | (p → ¬q) |
| C. | (¬p → ¬q) |
| D. | (¬p → q) |
| Answer» B. (p → ¬q) | |
| 56. |
¬ (p ↔ q) is logically equivalent to ________ |
| A. | q↔p |
| B. | p↔¬q |
| C. | ¬p↔¬q |
| D. | ¬q↔¬p |
| Answer» C. ¬p↔¬q | |
| 57. |
p ↔ q is logically equivalent to ________ |
| A. | (p → q) → (q → p) |
| B. | (p → q) ∨ (q → p) |
| C. | (p → q) ∧ (q → p) |
| D. | (p ∧ q) → (q ∧ p) |
| Answer» D. (p ∧ q) → (q ∧ p) | |
| 58. |
(p → r) ∨ (q → r) is logically equivalent to ________ |
| A. | (p ∧ q) ∨ r |
| B. | (p ∨ q) → r |
| C. | (p ∧ q) → r |
| D. | (p → q) → r |
| Answer» D. (p → q) → r | |
| 59. |
If A is “001100” and B is “010101” then what is the value of A (Ex-or) B? |
| A. | 000000 |
| B. | 111111 |
| C. | 001101 |
| D. | 011001 |
| Answer» E. | |
| 60. |
Let P (x) denote the statement “x >7.” Which of these have truth value true? |
| A. | P (0) |
| B. | P (4) |
| C. | P (6) |
| D. | P (9) |
| Answer» E. | |
| 61. |
(p → q) ∧ (p → r) is logically equivalent to ________ |
| A. | p → (q ∧ r) |
| B. | p → (q ∨ r) |
| C. | p ∧ (q ∨ r) |
| D. | p ∨ (q ∧ r) |
| Answer» B. p → (q ∨ r) | |
| 62. |
If a bit string contains {0, 1} only, having length 5 has no more than 2 ones in it. Then how many such bit strings are possible? |
| A. | 14 |
| B. | 12 |
| C. | 15 |
| D. | 16 |
| Answer» E. | |
| 63. |
The Ex-nor of this string “01010101” with “11111111” is? |
| A. | 10101010 |
| B. | 00110100 |
| C. | 01010101 |
| D. | 10101001 |
| Answer» D. 10101001 | |
| 64. |
What is the one’s complement of this string “01010100”? |
| A. | 10101010 |
| B. | 00110101 |
| C. | 10101011 |
| D. | 10101001 |
| Answer» D. 10101001 | |
| 65. |
If in a bits string of {0,1}, of length 4, such that no two ones are together. Then the total number of such possible strings are? |
| A. | 1 |
| B. | 5 |
| C. | 7 |
| D. | 4 |
| Answer» D. 4 | |
| 66. |
What is the 2’s complement of this string “01010100”? |
| A. | 10101010 |
| B. | 00110100 |
| C. | 10101100 |
| D. | 10101001 |
| Answer» D. 10101001 | |
| 67. |
Let P and Q be statements, then P<->Q is logically equivalent to __________ |
| A. | P<->~Q |
| B. | ~P<->Q |
| C. | ~P<->~Q |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 68. |
Let A: “010101”, B=?, If { A (Ex-or) B } is a resultant string of all ones then which of the following statement regarding B is correct? |
| A. | B is negation of A |
| B. | B is 101010 |
| C. | {A (and) B} is a resultant string having all zeroes |
| D. | All of the mentioned |
| Answer» E. | |
| 69. |
The compound statement A-> (A->B) is false, then the truth values of A, B are respectively _________ |
| A. | T, T |
| B. | F, T |
| C. | T, F |
| D. | F, F |
| Answer» D. F, F | |
| 70. |
How many bits string of length 4 are possible such that they contain 2 ones and 2 zeroes? |
| A. | 4 |
| B. | 2 |
| C. | 5 |
| D. | 6 |
| Answer» E. | |
| 71. |
Which of the following bits is the negation of the bits “010110”? |
| A. | 111001 |
| B. | 001001 |
| C. | 101001 |
| D. | 111111 |
| Answer» D. 111111 | |
| 72. |
Let P: We should be honest., Q: We should be dedicated., R: We should be overconfident. Then ‘We should be honest or dedicated but not overconfident.’ is best represented by? |
| A. | ~P V ~Q V R |
| B. | P ∧ ~Q ∧ R |
| C. | P V Q ∧ R |
| D. | P V Q ∧ ~R |
| Answer» E. | |
| 73. |
Which of the following option is suitable, if A is “10110110”, B is”11100000” and C is”10100000”? |
| A. | C=A or B |
| B. | C=~A |
| C. | C=~B |
| D. | C=A and B |
| Answer» E. | |
| 74. |
Let P: I am in Bangalore.; Q: I love cricket.; then q -> p(q implies p) is? |
| A. | If I love cricket then I am in Bangalore |
| B. | If I am in Bangalore then I love cricket |
| C. | I am not in Bangalore |
| D. | I love cricket |
| Answer» B. If I am in Bangalore then I love cricket | |
| 75. |
What is the value of x after this statement, assuming the initial value of x is 5? |
| A. | 1 |
| B. | 3 |
| C. | 0 |
| D. | 2 |
| Answer» D. 2 | |
| 76. |
The truth value ‘9 is prime then 3 is even’. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 77. |
Let P: I am in Delhi.; Q: Delhi is clean.; then q ^ p(q and p) is? |
| A. | Delhi is clean and I am in Delhi |
| B. | Delhi is not clean or I am in Delhi |
| C. | I am in Delhi and Delhi is not clean |
| D. | Delhi is clean but I am in Mumbai |
| Answer» B. Delhi is not clean or I am in Delhi | |
| 78. |
Let P: This is a great website, Q: You should not come back here. Then ‘This is a great website and you should come back here.’ is best represented by? |
| A. | ~P V ~Q |
| B. | P ∧ ~Q |
| C. | P V Q |
| D. | P ∧ Q |
| Answer» C. P V Q | |
| 79. |
Let P: If Sahil bowls, Saurabh hits a century.; Q: If Raju bowls, Sahil gets out on first ball. Now if P is true and Q is false then which of the following can be true? |
| A. | Raju bowled and Sahil got out on first ball |
| B. | Raju did not bowled |
| C. | Sahil bowled and Saurabh hits a century |
| D. | Sahil bowled and Saurabh got out |
| Answer» D. Sahil bowled and Saurabh got out | |
| 80. |
Which of the following represents: ~A (negation of A) if A stands for “I like badminton but hate maths”? |
| A. | I hate badminton and maths |
| B. | I do not like badminton or maths |
| C. | I dislike badminton but love maths |
| D. | I hate badminton or like maths |
| Answer» E. | |
| 81. |
Which of the following statements is the negation of the statements “4 is odd or -9 is positive”? |
| A. | 4 is even or -9 is not negative |
| B. | 4 is odd or -9 is not negative |
| C. | 4 is even and -9 is negative |
| D. | 4 is odd and -9 is not negative |
| Answer» D. 4 is odd and -9 is not negative | |
| 82. |
The compound statement A v ~(A ∧ B). |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 83. |
Which of the following is De-Morgan’s law? |
| A. | P ∧ (Q v R) Ξ (P ∧ Q) v (P ∧ R) |
| B. | ~(P ∧ R) Ξ ~P v ~R, ~(P v R) Ξ ~P ∧ ~R |
| C. | P v ~P Ξ True, P ∧ ~P Ξ False |
| D. | None of the mentioned |
| Answer» C. P v ~P Ξ True, P ∧ ~P Ξ False | |
| 84. |
~ A v ~ B is logically equivalent to? |
| A. | ~ A → ~ B |
| B. | ~ A ∧ ~ B |
| C. | A → ~B |
| D. | B V A |
| Answer» D. B V A | |
| 85. |
What is the dual of (A ∧ B) v (C ∧ D)? |
| A. | (A V B) v (C v D) |
| B. | (A V B) ^ (C v D) |
| C. | (A V B) v (C ∧ D) |
| D. | (A ∧ B) v (C v D) |
| Answer» C. (A V B) v (C ∧ D) | |
| 86. |
Which of the following satisfies commutative law? |
| A. | ∧ |
| B. | v |
| C. | ↔ |
| D. | All of the mentioned |
| Answer» E. | |
| 87. |
Negation of statement (A ∧ B) → (B ∧ C) is _____________ |
| A. | (A ∧ B) →(~B ∧ ~C) |
| B. | ~(A ∧ B) v ( B v C) |
| C. | ~(A →B) →(~B ∧ C) |
| D. | None of the mentioned |
| Answer» B. ~(A ∧ B) v ( B v C) | |
| 88. |
If P is always against the testimony of Q, then the compound statement P→(P v ~Q) is a __________ |
| A. | Tautology |
| B. | Contradiction |
| C. | Contingency |
| D. | None of the mentioned |
| Answer» B. Contradiction | |
| 89. |
If the truth value of A v B is true, then truth value of ~A ∧ B can be ___________ |
| A. | True if A is false |
| B. | False if A is false |
| C. | False if B is true and A is false |
| D. | None of the mentioned |
| Answer» B. False if A is false | |
| 90. |
The statement which is logically equivalent to A∧ (and) B is? |
| A. | A->B |
| B. | ~A ∧ ~ B |
| C. | A ∧ ~B |
| D. | ~(A->~B) |
| Answer» E. | |
| 91. |
Let P, Q, R be true, false true, respectively, which of the following is true? |
| A. | P∧Q∧R |
| B. | P∧~Q∧~R |
| C. | Q->(P∧R) |
| D. | P->(Q∧R) |
| Answer» D. P->(Q∧R) | |
| 92. |
If in a for it to be complete it is necessary for switch A to be closed and either of switch B or C to be closed, then which can be true? |
| A. | Switch A should in parallel with B and C is series to them |
| B. | Switch A should be in series with a parallel circuit of B and C |
| C. | All of the mentioned |
| D. | None of the mentioned |
| Answer» C. All of the mentioned | |
| 93. |
If there are ‘M’ switches in parallel numbered from 1, 2, …, M. For circuit to be complete and bulb to glow which of the following is necessary |
| A. | 1∧ 2∧ 3 ∧ … ∧M should be on |
| B. | 1∧ 2∧ 3 ∧ … ∧M should be off |
| C. | 1 v 2 v 3 v … v M should be on |
| D. | None of the mentioned |
| Answer» D. None of the mentioned | |
| 94. |
Consider the following statements. |
| A. | A->B->C |
| B. | B∧(C->A) |
| C. | C->B∧A |
| D. | B<->A∧C |
| Answer» C. C->B∧A | |
| 95. |
Let P, Q, R be true, false, false, respectively, which of the following is true? |
| A. | P∧(Q∧~R) |
| B. | (P->Q)∧~R |
| C. | Q<->(P∧R) |
| D. | P<->(QvR) |
| Answer» D. P<->(QvR) | |
| 96. |
“Match will be played only if it is not a humid day.” The negation of this statement is? |
| A. | Match will be played but it is a humid day |
| B. | Match will be played or it is a humid day |
| C. | All of the mentioned statement are correct |
| D. | None of the mentioned |
| Answer» B. Match will be played or it is a humid day | |
| 97. |
The statement (~P<->Q)∧~Q is true when? |
| A. | P: True Q: False |
| B. | P: True Q: True |
| C. | P: False Q: True |
| D. | P: False Q: False |
| Answer» B. P: True Q: True | |
| 98. |
If there are ‘M’ switches in series numbered from 1, 2, …, M. For circuit to be complete and bulb to glow which of the following is necessary? |
| A. | 1∧ 2∧ 3 ∧ … ∧M should be on |
| B. | 1∧ 2∧ 3 ∧ … ∧M should be off |
| C. | 1 v 2 v 3 v … v M should be on |
| D. | None of the mentioned |
| Answer» B. 1∧ 2∧ 3 ∧ … ∧M should be off | |
| 99. |
In the circuit shown the lamp will be glowing if _________ |
| A. | P: True, Q: False |
| B. | P: True, Q: True |
| C. | P: False, Q: False |
| D. | None of the mentioned |
| Answer» B. P: True, Q: True | |
| 100. |
The truth value of ‘4+3=7 or 5 is not prime’. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |