Logics MCQ

Test your knowledge with important Logics MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Logics MCQs at Bissoy

• “Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that __________
  ক

  Parul is out for trip

  খ

  Raju is playing chess

  গ

  Parul is out for a trip and Raju is playing chess

  ঘ

  Parul is out for a trip or Raju is playing chess
• What rules of inference are used in this argument? “Jay is an awesome student. Jay is also a good dancer. Therefore, Jay is an awesome student and a good dancer.”
  ক

  Conjunction

  খ

  Modus ponens

  গ

  Disjunctive syllogism

  ঘ

  Simplification
• The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?
  ক

  p ∨ r

  খ

  p ∨ s

  গ

  p ∨ q

  ঘ

  q ∨ r
• What rules of inference are used in this argument? “It is either colder than Himalaya today or the pollution is harmful. It is hotter than Himalaya today. Therefore, the pollution is harmful.”
  ক

  Conjunction

  খ

  Modus ponens

  গ

  Disjunctive syllogism

  ঘ

  Hypothetical syllogism
• What rules of inference are used in this argument? “All students in this science class has taken a course in physics” and “Marry is a student in this class” imply the conclusion “Marry has taken a course in physics.”
  ক

  Universal instantiation

  খ

  Universal generalization

  গ

  Existential instantiation

  ঘ

  Existential generalization
• What rule of inference is used in this argument? “If I go for a balanced diet, then I will be fit. If I will be fit, then I will remain healthy. Therefore, if I go for a balanced diet, then I will remain healthy.”
  ক

  Modus tollens

  খ

  Modus ponens

  গ

  Disjunctive syllogism

  ঘ

  Hypothetical syllogism
• What rule of inference is used here? “It is cloudy and drizzling now. Therefore, it is cloudy now.”
  ক

  Addition

  খ

  Simplification

  গ

  Resolution

  ঘ

  Conjunction
• Which rule of inference is used, ”Bhavika will work in an enterprise this summer. Therefore, this summer Bhavika will work in an enterprise or he will go to beach.”
  ক

  Simplification

  খ

  Conjunction

  গ

  Addition

  ঘ

  Disjunctive syllogism
• Which rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”
  ক

  Modus tollens

  খ

  Conjunction

  গ

  Hypothetical syllogism

  ঘ

  Simplification
• Which rule of inference is used in each of these arguments, “If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded.”
  ক

  Modus tollens

  খ

  Modus ponens

  গ

  Disjunctive syllogism

  ঘ

  Simplification
• Find a counterexample of ∀x∀y(xy > y), where the domain for all variables consists of all integers.
  ক

  x = -1, y = 17

  খ

  x = -2 y = 8

  গ

  Both x = -1, y = 17 and x = -2 y = 8

  ঘ

  Does not have any counter example
• Determine the truth value of ∃n∃m(n + m = 5 ∧ n − m = 2) if the domain for all variables consists of all integers.
  ক

  True

  খ

  False
• 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.”
  ক

  ∃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

  খ

  ∃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

  গ

  ∀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

  ঘ

  ∃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
• Express, “The difference of a real number and itself is zero” using required operators.
  ক

  ∀x(x − x! = 0)

  খ

  ∀x(x − x = 0)

  গ

  ∀x∀y(x − y = 0)

  ঘ

  ∃x(x − x = 0)
• 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.
  ক

  All students does not like South Indian dishes.

  খ

  Amit does not like South Indian people.

  গ

  Amit does not like South Indian dishes.

  ঘ

  Amit does not like some dishes.
• 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.”
  ক

  ∀x L(x, Joy)

  খ

  ∀y L(Joy,y)

  গ

  ∃y∀x L(x, y)

  ঘ

  ∃x ¬L(Joy, x)
• 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).
  ক

  True

  খ

  False
• “The product of two negative real numbers is not negative.” Is given by?
  ক

  ∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))

  খ

  ∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

  গ

  ∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))

  ঘ

  ∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))
• Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable.
  ক

  For all real number x there exists a real number y such that x is less than y

  খ

  For every real number y there exists a real number x such that x is less than y

  গ

  For some real number x there exists a real number y such that x is less than y

  ঘ

  For each and every real number x and y such that x is less than y
• Let Q(x, y) denote “M + A = 0.” What is the truth value of the quantifications ∃A∀M Q(M, A).
  ক

  True

  খ

  False
• (p → r) ∨ (q → r) is logically equivalent to ________
  ক

  (p ∧ q) ∨ r

  খ

  (p ∨ q) → r

  গ

  (p ∧ q) → r

  ঘ

  (p → q) → r
• (p → q) ∧ (p → r) is logically equivalent to ________
  ক

  p → (q ∧ r)

  খ

  p → (q ∨ r)

  গ

  p ∧ (q ∨ r)

  ঘ

  p ∨ (q ∧ r)
• p ↔ q is logically equivalent to ________
  ক

  (p → q) → (q → p)

  খ

  (p → q) ∨ (q → p)

  গ

  (p → q) ∧ (q → p)

  ঘ

  (p ∧ q) → (q ∧ p)
• p ∧ q is logically equivalent to ________
  ক

  ¬ (p → ¬q)

  খ

  (p → ¬q)

  গ

  (¬p → ¬q)

  ঘ

  (¬p → q)
• ¬ (p ↔ q) is logically equivalent to ________
  ক

  q↔p

  খ

  p↔¬q

  গ

  ¬p↔¬q

  ঘ

  ¬q↔¬p
• p ∨ q is logically equivalent to ________
  ক

  ¬q → ¬p

  খ

  q → p

  গ

  ¬p → ¬q

  ঘ

  ¬p → q
• p → q is logically equivalent to ________
  ক

  ¬p ∨ ¬q

  খ

  p ∨ ¬q

  গ

  ¬p ∨ q

  ঘ

  ¬p ∧ q
• The compound propositions p and q are called logically equivalent if ________ is a tautology.
  ক

  p ↔ q

  খ

  p → q

  গ

  ¬ (p ∨ q)

  ঘ

  ¬p ∨ ¬q
• What are the inverse of the conditional statement “If you make your notes, it will be a convenient in exams.”
  ক

  “If you make notes, then it will be a convenient in exams.”

  খ

  “If you do not make notes, then it will not be a convenient in exams.”

  গ

  “If it will not be a convenient in exams, then you did not make your notes.”

  ঘ

  “If it will be a convenient in exams, then you make your notes
• What are the contrapositive of the conditional statement “Medha will find a decent job when she labour hard.”?
  ক

  “If Medha labour hard, then she will find a decent job.”

  খ

  “If Medha will not find a decent job, then she not labour hard.”

  গ

  “If Medha will find a decent job, then she labour hard.”

  ঘ

  “If Medha not labour hard, then she will not find a decent job.”