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Test: Propositional & First Order Logic- 1 - Question 1

What is the logical translation of the following statement?

"None of my friends are perfect."

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Test: Propositional & First Order Logic- 1 - Question 2

Let # be a binary operator defined as X # Y = X′ + Y′ where X and Y are Boolean variables. Consider the following two statements.

S1: (P # Q) # R = P # (Q # R)

S2: Q # R = R # Q

Which of the following is/are true for the Boolean variables P, Q and R?

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Test: Propositional & First Order Logic- 1 - Question 3

What is the correct translation of the following statement into mathematical logic?

“Some real numbers are rational”

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Test: Propositional & First Order Logic- 1 - 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))

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Test: Propositional & First Order Logic- 1 - 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))?

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Test: Propositional & First Order Logic- 1 - 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

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Test: Propositional & First Order Logic- 1 - Question 7

In propositional logic P ↔ Q is equivalent to (Where ~ denotes NOT):

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Test: Propositional & First Order Logic- 1 - Question 8

**Q. Which of the above two are equivalent?**

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Test: Propositional & First Order Logic- 1 - Question 9

Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton, and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such that equivalent (a, b) means a and b are equivalent. Which of the following first order logic statements represents the following: Each finite state automaton has an equivalent pushdown automaton.

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Test: Propositional & First Order Logic- 1 - Question 10

P and Q are two propositions. Which of the following logical expressions are equivalent?

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Test: Propositional & First Order Logic- 1 - Question 11

Let Graph(x) be a predicate which denotes that x is a graph. Let Connected(x) be a predicate which denotes that x is connected. Which of the following first order logic sentences DOES NOT represent the statement: “Not every graph is connected”?

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Test: Propositional & First Order Logic- 1 - Question 12

Which of the following is TRUE about formulae in Conjunctive Normal Form?

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Test: Propositional & First Order Logic- 1 - Question 13

The following propositional statement is (P → (Q v R)) → ((P ^ Q) → R)

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Test: Propositional & First Order Logic- 1 - Question 14

Which one of the following Boolean expressions is NOT a tautology?

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Test: Propositional & First Order Logic- 1 - Question 15

The CORRECT formula for the sentence, “not all rainy days are cold” is

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Test: Propositional & First Order Logic- 1 - Question 16

Which one of the first order predicate calculus statements given below correctly express the following English statement?

Tigers and lions attack if they are hungry or threatened.

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Test: Propositional & First Order Logic- 1 - Question 17

Consider the following propositional statements:

P1 : ((A ∧ B) → C)) ≡ ((A → C) ∧ (B → C))

P2 : ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C))

which one of the following is true?

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Test: Propositional & First Order Logic- 1 - Question 18

A logical binary relation □ ,is defined as follows

**Q. Let ~ be the unary negation (NOT) operator, with higher precedence than □. Which one of the following is equivalent to A∧B ?**

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Test: Propositional & First Order Logic- 1 - Question 19

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?

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Test: Propositional & First Order Logic- 1 - Question 20

What is the first order predicate calculus statement equivalent to the following?

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