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⇱ Quiz about Propositional Logic PYQ Quiz GATE CS

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Question 1

What is the correct translation of the following statement into mathematical logic? “Some real numbers are rational” 

👁 Image
 

  • A

  • B

  • C

  • D

Question 2

What is the logical translation of the following statement? 

 "None of my friends are perfect."
👁 gatecs201311

  • A

  • B

  • C

  • D

Question 3

Which one of the following is NOT logically equivalent to ¬∃x(∀y(α)∧∀z(β))?

  • ∀x(∃z(¬β)->∀y(α))

  • ∀x(∀z(β)->∃y(¬α))

  • ∀x(∀y(α)->∃z(¬β))

  • ∀x(∃y(¬α)->∃z(¬β))

Question 4

Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate? 


 P(x) = ¬(x=1)∧∀y(∃z(x=y*z)⇒(y=x)∨(y=1))

  • P(x) being true means that x is a number other than 1

  • P(x) is always true irrespective of the value of x

  • P(x) being true means that x has exactly two factors other than 1 and x 

  • P(x) being true means that x is a prime number

Question 5

Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula ∀x∃y∃t(¬F(x, y, t))?

  • Everyone can fool some person at some time

  • No one can fool everyone all the time

  • Everyone cannot fool some person all the time

  • No one can fool some person at some time

Question 6

Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: G(x): x is a gold ornament S(x): x is a silver ornament P(x): x is precious

  • ∀x(P(x)→(G(x)∧S(x)))

  • ∀x((G(x)∧S(x))→P(x))

  • ∃x((G(x)∧S(x))→P(x)

  • ∀x((G(x)∨S(x))→P(x))

Question 7

Consider the following first order logic formula in which R is a binary relation symbol.

∀x∀y (R(x, y)  => R(y, x))

The formula is  

  • satisfiable and valid

  • satisfiable and so is its negation

  • unsatisfiable but its negation is valid

  • satisfiable but its negation is unsatisfiable

Question 8

The binary operator ≠ is defined by the following truth table

👁 GATE-CS-2015-Q65

Which one of the following is true about the binary operator ≠?

  • Both commutative and associative

  • Commutative but not associative

  • Not commutative but associative

  • Neither commutative nor associative

Question 9

Choose the correct choice(s) regarding the following proportional logic assertion S: 

S:((P∧Q)→R)→((P∧Q)→(Q→R))

  • S is neither a tautology nor a contradiction

  • S is a tautology

  • S is a contradiction

  • The antecedent of S is logically equivalent to the consequent of S

Question 10

Let P, Q and R be three atomic prepositional assertions. Let X denote (P v Q) → R and Y denote (P → R) v (Q → R). Which one of the following is a tautology?

  • X ≡ Y

  • X → Y

  • Y → X

  • ¬ Y → X

There are 41 questions to complete.

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