**Ques.** Which of the following is not a statement

(a) Every set is a finite set

(b) 8 is less than 6

(c) Where are you going ?

(d) The sum of interior angles of a triangle is 180 degrees

Ans. (c)

**Ques. **Which of the following is not a statement

(a) Please do me a favour

(b) 2 is an even integer

(c) 2 + 1 = 3

(d) The number 17 is prime

Ans. (a)

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**Ques. **Which of the following is an open statement

(a) *x* is a natural number

(b) Give me a glass of water

(c) Wish you best of luck

(d) Good morning to all

Ans. (a)

**Ques.** If *p*, *q*, *r* are simple propositions with truth values T, F, T, then the truth value of (~ p q) ~ r p is

(a) True

(b) False

(c) True if *r* is false

(d) True if *q* is true

Ans. (a)

**Ques. **If (p ~ r) (q r) is false and *q* and *r* are both false, then *p* is

(a) True

(b) False

(c) May be true or false

(d) Data insufficient

Ans. (a)

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**Ques. **(p ~ q) (~ p q) is

(a) A contradiction

(b) A tautology

(c) Either (a) or (b)

(d) Neither (a) nor (b)

Ans. (a)

**Ques. **Which of the following is not logically equivalent to the proposition : “A real number is either rational or irrational”.

(a) If a number is neither rational nor irrational then it is not real

(b) If a number is not a rational or not an irrational, then it is not real

(c) If a number is not real, then it is neither rational nor irrational

(d) If a number is real, then it is rational or irrational

Ans. (b)

**Ques. **If *p* : It rains today, *q* : I go to school, *r* : I shall meet any friends and *s* : I shall go for a movie, then which of the following is the proposition :

If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.

(a) ~ (p q) -> (r s)

(b) ~ (p ~ q) -> (r s)

(c) ~ (p q) -> (r s)

(d) None of these

Ans. (a)

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**Ques. **The propositions (p ~ p) (~ p p) is a

(a) Tautology and contradiction

(b) Neither tautology nor contradiction

(c) Contradiction

(d) Tautology

Ans. (c)

**Ques.** If p (q r) is false, then the truth values of *p*, *q*, *r* are respectively

(a) T, F, F

(b) F, F, F

(c) F, T, T

(d) T, T, F

Ans. (a)

**Ques.** If p (~ p q) is false, the truth values of *p* and *q* are respectively

(a) F, T

(b) F, F

(c) T, T

(d) T, F

Ans. (d)

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**Ques. **(p ~ q) (~ p q) is

(a) A tautology

(b) A contradiction

(c) Both a tautology and a contradiction

(d) Neither a tautology nor a contradiction

Ans. (b)

**Ques. **Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

(a) If a number is not a prime then it is odd

(b) If a number is not a prime then it is odd

(c) If a number is not odd then it is not a prime

(d) If a number is not odd then it is a prime

Ans. (b)

**Ques. **~ (p (~q)) is equal to

(a) ~ p q

(b) (~p) q

(c) ~ p ~ p

(d) ~p ~ q

Ans. (b)

**Ques. **Which of the following is logically equivalent to ~ (~ p q)

(a) p q

(b) p ~ q

(c) ~ p q

(d) ~ p ~ q

Ans. (d)

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**Ques. **The conditional (p q) p is

(a) A tautology

(b) A fallacy *i.e.*, contradiction

(c) Neither tautology nor fallacy

(d) None of these

Ans. (a)

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