Mathematical Logic Questions

Q 1. Which of the following is not a statement
A. Where are you going ?
B. 8 is less than 6
C. Every set is a finite set
D. The sum of interior angles of a triangle is 180 degrees

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Answer:-A. Where are you going ?

Q 2. 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

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Answer:-A. Please do me a favour

Q 3. 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

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Answer:-A.  x is a natural number

Q 4. 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

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Answer:-A. True

Q 5. If (p  ~ r)  (q  r) is false and q and r are both false, then p is
A. False
B. True
C. May be true or false
D. Data insufficient

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Answer:-B. True

Q 6. (p  ~ q)  (~ p  q) is
A. A contradiction
B. A tautology
C. Either (a) or (b)
D. Neither (a) nor (b)

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Answer:-A. A contradiction

Q 7. 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

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Answer:-B. If a number is not a rational or not an irrational, then it is not real

Q 8. 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

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Answer:-A. ~ (p  q) -> (r  s)

Q 9. The propositions (p  ~ p)  (~ p  p) is a
A. Tautology and contradiction
B. Neither tautology nor contradiction
C. Contradiction
D. Tautology

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Answer:-C. Contradiction

Q 10. If p  (q  r) is false, then the truth values of p, q, r are respectively
A. F, F, F
B. T, F, F
C. F, T, T
D. T, T, F

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Answer:-B. T, F, F

Q 11. 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

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Answer:-D. T, F

Q 12. (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

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Answer:-B. A contradiction

Q 13. 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

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Answer:-B. If a number is not a prime then it is odd

Q 14. ~ (p  (~q)) is equal to
A. ~ p  q
B. (~p)  q
C. ~ p  ~ p
D. ~p  ~ q

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Answer:-B. (~p)  q

Q 15. 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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Answer:-

Q 16. The conditional (p  q)  p is
A. A fallacy i.e., contradiction
B. A tautology
C. Neither tautology nor fallacy
D. None of these

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Answer:-B. A tautology