MATHEMATICAL REASONING PART 3
QUIZ  /  MATHEMATICAL REASONING  /  MATHEMATICAL REASONING PART 3

  • 1.
      Which of the following Is logically equivalent to ̴ ( ̴ p →q) ?

  • p ^ q
  • p ^ ̴ q
  • ̴ p ^ q
  • ̴ p ^ ̴ q

  • 2.
      Which of the following Is a contradiction ?

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

  • 3.
      The negative of the proposition : "if a number is divisible By 15 then it is divisible by 5 or 3"

  • If a number is divisible by 15 and it is not divisible by 5 and 3
  • A number is divisible by 15 and it is not divisible by 5 and 3
  • A number is divisible by 15 and it is not divisible by 5 or 3
  • A number is not divisible by 15 or it is not divisible by 5 and 3

  • 4.
      ~(~p)⟷p is

  • A tautology
  • A contradiction
  • Neither a contradiction nor a tautology
  • None of these

  • 5.
      Consider the proposition : “ if we control population growth, We prosper”. Negative of this proposition is

  • If we do not control population growth, we prosper
  • If we control population, we do not prosper
  • We control population but we do not prosper
  • We do not control population but we prosper

  • 6.
      The negation of q ˅ ̴ ( p ^ r) is

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

  • 7.
      The negation of p ^ ̴ ( q ^ r) is

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

  • 8.
      The contra positive of ( ̴ p^ q ) → ̴ r is

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

  • 9.
      P → q Is logically equivalent to

  • p ^ ̴ q
  • ̴ p → ̴ q
  • ̴ q → ̴ p
  • None of these

  • 10.
      Which of the following is logically equivalent to ̴ ( p ↔ q) ?

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

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