MCQOPTIONS
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MCQOPTIONS
This section includes 20 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find a counterexample of ∀x∀y(xy > y), where the domain for all variables consists of all integers. |
| A. | x = -1, y = 17 |
| B. | x = -2 y = 8 |
| C. | Both x = -1, y = 17 and x = -2 y = 8 |
| D. | Does not have any counter example |
| Answer» D. Does not have any counter example | |
| 2. |
Determine the truth value of ∃n∃m(n + m = 5 ∧ n − m = 2) if the domain for all variables consists of all integers. |
| A. | True |
| B. | False |
| Answer» C. | |
| 3. |
Use quantifiers and predicates with more than one variable to express, “There is a pupil in this lecture who has taken at least one course in Discrete Maths.” |
| A. | ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures |
| B. | ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class |
| C. | ∀x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures |
| D. | ∃x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures |
| Answer» B. ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class | |
| 4. |
Express, “The difference of a real number and itself is zero” using required operators. |
| A. | ∀x(x − x! = 0) |
| B. | ∀x(x − x = 0) |
| C. | ∀x∀y(x − y = 0) |
| D. | ∃x(x − x = 0) |
| Answer» C. ∀x∀y(x − y = 0) | |
| 5. |
Let T (x, y) mean that student x likes dish y, where the domain for x consists of all students at your school and the domain for y consists of all dishes. Express ¬T (Amit, South Indian) by a simple English sentence. |
| A. | All students does not like South Indian dishes. |
| B. | Amit does not like South Indian people. |
| C. | Amit does not like South Indian dishes. |
| D. | Amit does not like some dishes. |
| Answer» E. | |
| 6. |
Let L(x, y) be the statement “x loves y,” where the domain for both x and y consists of all people in the world. Use quantifiers to express, “Joy is loved by everyone.” |
| A. | ∀x L(x, Joy) |
| B. | ∀y L(Joy,y) |
| C. | ∃y∀x L(x, y) |
| D. | ∃x ¬L(Joy, x) |
| Answer» B. ∀y L(Joy,y) | |
| 7. |
Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4). |
| A. | True |
| B. | False |
| Answer» C. | |
| 8. |
“The product of two negative real numbers is not negative.” Is given by? |
| A. | ∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0)) |
| B. | ∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0)) |
| C. | ∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0)) |
| D. | ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0)) |
| Answer» E. | |
| 9. |
Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable. |
| A. | For all real number x there exists a real number y such that x is less than y |
| B. | For every real number y there exists a real number x such that x is less than y |
| C. | For some real number x there exists a real number y such that x is less than y |
| D. | For each and every real number x and y such that x is less than y |
| Answer» B. For every real number y there exists a real number x such that x is less than y | |
| 10. |
Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A). |
| A. | True |
| B. | False |
| Answer» C. | |
| 11. |
DETERMINE_THE_TRUTH_VALUE_OF_‚ÄÖ√Ñ√∂‚ÀւĆ‚ÀÖ√¢N‚ÄÖ√Ñ√∂‚ÀւĆ‚ÀÖ√¢M(N_+_M_=_5_‚ÄÖ√Ñ√∂‚ÀւĆ‚ÀÖ√º_N_‚ÄÖ√Ñ√∂‚ÀւĆ‚Àւ†_M_=_2)_IF_THE_DOMAIN_FOR_ALL_VARIABLES_CONSISTS_OF_ALL_INTEGERS.?$# |
| A. | True |
| B. | False |
| Answer» C. | |
| 12. |
Find_a_counterexample_of_∀x∀y(xy_>_y),_where_the_domain_for_all_variables_consists_of_all_integers.$# |
| A. | x = -1, y = 17 |
| B. | x = -2 y = 8 |
| C. | Both a and b |
| D. | Does not have any counter example |
| Answer» D. Does not have any counter example | |
| 13. |
Use quantifiers and predicates with more than one variable to express, ‚Äö√Ñ√∂‚àö√ë‚àö‚à´There is a pupil in this lecture who has taken at least one course in Discrete Maths.‚Äö√Ñ√∂‚àö√ë‚àöœ?# |
| A. | ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures |
| B. | ∃x∃yP (x, y), where P (x, y) is “x has taken y,” the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class |
| C. | ∀x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures |
| D. | ∃x∀yP(x, y), where P (x, y) is “x has taken y,” the domain for x consists of all pupil in this class, and the domain for y consists of all Discrete Maths lectures |
| Answer» B. ‚Äö√Ñ√∂‚àö‚Ć‚àö√¢x‚Äö√Ñ√∂‚àö‚Ć‚àö√¢yP (x, y), where P (x, y) is ‚Äö√Ñ√∂‚àö√ë‚àö‚à´x has taken y,‚Äö√Ñ√∂‚àö√ë‚àöœÄ the domain for x consists of all Discrete Maths lectures, and the domain for y consists of all pupil in this class | |
| 14. |
Express, “The difference of a real number and itself is zero” using required operators.$ |
| A. | ∀x(x − x! = 0) |
| B. | ∀x(x − x = 0) |
| C. | ∀x∀y(x − y = 0) |
| D. | ∃x(x − x = 0) |
| Answer» C. ‚Äö√Ñ√∂‚àö‚Ć‚àö√ëx‚Äö√Ñ√∂‚àö‚Ć‚àö√ëy(x ‚Äö√Ñ√∂‚àö‚Ć‚àö‚↠y = 0) | |
| 15. |
Let T (x, y) mean that student x likes dish y, where the domain for x consists of all students at your school and the domain for y consists of all dishes. Express ¬T (Amit, South Indian) by a simple English sentence.$ |
| A. | All students does not like South Indian dishes. |
| B. | Amit does not like South Indian people. |
| C. | Amit does not like South Indian dishes. |
| D. | Amit does not like some dishes. |
| Answer» E. | |
| 16. |
Let L(x, y) be the statement “x loves y,” where the domain for both x and y consists of all people in the world.$ |
| A. | |
| B. | ∀x L(x, Joy) |
| C. | ∀y L(Joy,y) |
| Answer» B. ‚Äö√Ñ√∂‚àö‚Ć‚àö√ëx L(x, Joy) | |
| 17. |
Let Q(x, y) be the statement “x + y = x − y.” If the domain for both variables consists of all integers, what is the truth value of ∃xQ(x, 4).$ |
| A. | True |
| B. | False |
| Answer» C. | |
| 18. |
“The product of two negative real numbers is not negative.” Is given by?$ |
| A. | ∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0)) |
| B. | ∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0)) |
| C. | ∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0)) |
| D. | ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0)) |
| Answer» E. | |
| 19. |
Translate ∀x∃y(x < y) in English, considering domain as real number for both the variable.$ |
| A. | For all real number x there exists a real number y such that x is less than y |
| B. | For every real number y there exists a real number x such that x is less than y |
| C. | For some real number x there exists a real number y such that x is less than y |
| D. | For each and every real number x and y such that x is less than y |
| Answer» B. For every real number y there exists a real number x such that x is less than y | |
| 20. |
Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A) |
| A. | True |
| B. | False |
| Answer» C. | |