MATHEMATICAL REASONING PART 4
QUIZ  /  MATHEMATICAL REASONING  /  MATHEMATICAL REASONING PART 4

  • 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 logically equivalent to (p ^ q)?

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

  • 3.
      The contra positive of 2x + 3 = 9 => x ≠ 4 is

  • x= 4 => 2x +3 ≠9
  • x= 4 => 2x +3 =9
  • x ≠ 4 => 2x +3 ≠9
  • x ≠ 4 => 2x +3 =9

  • 4.
      The proposition ( p → ̴ p ) ^ ( ̴ p →p ) is a

  • Tautology
  • Contradiction
  • Neither a tautology nor a contradiction
  • Tautology and contradiction

  • 5.
      Consider the following statements p : I shall pass q: I study The symbolic representation of the proposition “ I shall Pass iff I study” is

  • p→ q
  • q→ p
  • p→ ̴ q
  • p↔ q

  • 6.
      The proposition p → ̴ ( p ^ ̴ q) is

  • A contradiction
  • a tautology
  • either a tautology or a contradiction
  • neither a tautology nor a contradiction

  • 7.
      ̴ ( p ˅ q ) ˅ ( ̴ p ^ q ) is logically equivalent to

  • ~p
  • p
  • q
  • ~q

  • 8.
      The negation of the compound proposition p ˅ ( ̴ p ˅ q) is ?

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

  • 9.
      Let p be the proposition : mathematics is interesting And let q be the proposition that mathematics is difficult then the symbol p ^ q means?

  • Mathematics Is interesting implies that mathematics is difficult
  • Mathematics Is interesting implies and is implied by Mathematics is difficult
  • Mathematics is interesting and Mathematics is difficult
  • Mathematics is interesting or Mathematics is difficult

  • 10.
      The inverse of the proposition ( p ^ ̴ q ) → r is

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

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