Propositional and First Order Logic.

Question 71

Which of the following arguments are valid ?

(a)“If Gora gets the job and works hard, then he will be promoted. If Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard”.

(b)“Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty”. 

(c)If n is a real number such that n>1, then n²>1. Suppose that n²>1, then n>1.

• (a) and (c)

• (b) and (c)

• (a), (b) and (c)

• (a) and (b)

Question 72

Match the following terms:

• (1)
• (2)
• (3)
• (4)

Question 73

Consider the compound propositions given below as: (a)p ∨ ~(p ∧ q) (b)(p ∧ ~q) ∨ ~(p ∧ q) (c)p ∧ (q ∨ r) Which of the above propositions are tautologies?

• (a) and (c)
• (b) and (c)
• (a) and (b)
• only (a)

Question 74

“If my computations are correct and I pay the electric bill, then I will run out of money. If I don’t pay the electric bill, the power will be turned off. Therefore, if I don’t run out of money and the power is still on, then my computations are incorrect.” Convert this argument into logical notations using the variables c, b, r, p for propositions of computations, electric bills, out of money and the power respectively. (Where ¬ means NOT)

• if (c Λ b)→r and ¬b→p, then (¬r Λ p)→¬c
• if (c ∨ b)→r and ¬b→¬p, then (r Λ p)→c
• if (c Λ b)→r and ¬p→b, then (¬r ∨ p)→¬c
• if (c ∨ b)→r and ¬b→¬p, then (¬r Λ p)→¬c

Question 75

Match the following:

• (1)
• (2)
• (3)
• (4)

Question 76

Consider a proposition given as : “ x ≥ 6, if x² ≥ 5 and its proof as: If x ≥ 6, then x² = x.x ≥ 6.6 = 36 ≥ 25 Which of the following is correct w.r.to the given proposition and its proof? (a)The proof shows the converse of what is to be proved. (b)The proof starts by assuming what is to be shown. (c)The proof is correct and there is nothing wrong.

• (a) only
• (c) only
• (a) and (b)
• (b) only

Question 77

A horn clause is __________.

• A clause in which no variables occur in the expression
• A clause that has at least one negative literal
• A disjunction of a number of literals
• A clause that has at most one positive literal

Question 78

In Propositional Logic, given P and P → Q, we can infer __________.

• ~ Q
• Q
• P ∧ Q
• ~ P ∧ Q

Question 79

Which of the following is false for the programming language PROLOG?

• A PROLOG variable can only be assigned to a value once
• PROLOG is a strongly typed language
• The scope of a variable in PROLOG is a single clause or rule
• The scope of a variable in PROLOG is a single query

Question 80

Which one of the following is true?

• The resolvent of two Horn clauses is not a Horn clause
• The resolvent of two Horn clauses is a Horn clause
• If we resolve a negated goal G against a fact or rule A to get clause C then C has positive literal or non-null goal
• If we resolve a negated goal G against a fact or rule A to get clause C then C has positive literal or null goal