MATHEMATICAL REASONING PART 2
QUIZ  /  MATHEMATICAL REASONING  /  MATHEMATICAL REASONING PART 2

  • 1.
      Which of the following propositions is a tautology?

  • ( ̴ p ˅ ̴ q) ˅ (p ˅ ̴ q)
  • ( ̴ p ˅ ̴ q) ^ (p ˅ ̴ q)
  • ̴ p^( ̴ p ˅ ̴ q)
  • ̴ q^( ̴ p ˅ ̴ q)

  • 2.
      Which of the following proposition is tautology ?

  • ̴ (p →q ) ˅ (p ^ ̴ q)
  • (p → q)→ (p ^ ̴ q)
  • (p → q) ˅ (p ^ ̴ q)
  • ( p → q) ^ (p ^ ̴ q)

  • 3.
      Which of the following propositions is a contradiction?

  • ( ̴ p ˅ ̴ q ) ˅ ( p ˅ ̴ q)
  • (p → q) ˅ ( p ^ ̴ q)
  • ( ̴ p ^ q) ^ ( ̴ q)
  • ( ̴ p ^ q) ˅ ( ̴ q)

  • 4.
      P ^ q → p is

  • a tautology
  • A contradiction
  • Neither a tautology n or a contradiction
  • None of these

  • 5.
      Which of the following is false?

  • p ˅ ̴ p Is a tautology
  • ̴ ( ̴ p) ↔ p is a tautology
  • ( p ^ ( p → q ) → p is a contradiction
  • P ^ ̴ p is a contradiction

  • 6.
      Given that water freezes below zero degree Celsius Consider the following statements: p: water froze this morning q: this morning temperature was below 0˚c

  • p and q are logically equivalent
  • p is the inverse of q
  • p is the converse of q
  • p is the contrapositive of q

  • 7.
      If p, q, r have truth values T,F,T respectively, which Of the following is true?

  • ( p → q ) ^ r
  • (p → q) ^ ̴ r
  • (p ^ q ) ^ (p ˅ r)
  • q→ (p ^ r)

  • 8.
      If p → ( q ˅ r) is false then the truth values of p, q, r are respectively

  • T, T,T
  • F,T,T
  • F,F,F
  • T,F,F

  • 9.
      The negation of the proposition q˅ ̴ (p ^ r ) is

  • ̴ q ˅ (p ^ r )
  • ̴ q ^ (p ^ r )
  • ̴ p ˅ ̴ q ˅ ̴ r
  • None of these

  • 10.
      Which of the following is logically equivalent to p ^ q.

  • p → ̴ q
  • ̴ p ˅ ̴ q
  • ̴ (p → ̴ q)
  • ̴ ( ̴ p ^ ̴ q)

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