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Nexus of Logic: A Cognitive & Analytical Assessment

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1.Which of the following propositions is logically equivalent to "If it rains, the ground gets wet"?
  • 1.If the ground does not get wet, it does not rain
  • 2.If it rains, the ground will not get wet
  • 3.If the ground gets wet, it rains
  • 4.Unless it rains, the ground will not get wet ✓
2.Identify the valid conclusion from the following premises: All cats are mammals. All mammals are animals.
  • 1.All animals are cats
  • 2.Some animals are not cats
  • 3.No cats are animals
  • 4.All cats are animals ✓
3.In the statement "Either Tom or Jerry will win the race," which logical operation is primarily used?
  • 1.Conjunction
  • 2.Negation
  • 3.Implication
  • 4.Disjunction ✓
4.What is the contrapositive of the statement "If the sky is overcast, then it will rain"?
  • 1.If it does not rain, the sky is not overcast
  • 2.If the sky is not overcast, it will rain
  • 3.If it rains, the sky is not overcast
  • 4.If it does not rain, then the sky is not overcast ✓
5.Which of the following statements is an example of a tautology?
  • 1.The apple is red or it is not red
  • 2.The cat is on the mat and it is not raining
  • 3.If I win the lottery, I will be happy
  • 4.It is raining or it is not raining ✓

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6.If "All A are B" and "Some B are C," which conclusion cannot be correctly inferred?
  • 1.Some A are C
  • 2.Some C are A
  • 3.All C are A
  • 4.Some B are A ✓
7.Which operation shows the logical equivalence in "p AND q"?
  • 1.q AND p
  • 2.NOT (p OR q) ✓
  • 3.p OR NOT q
  • 4.NOT p AND q
8.From the premise "If Sally dances, then Tom sings," which is the inverse?
  • 1.If Sally does not dance, Tom sings
  • 2.If Tom sings, Sally dances
  • 3.If Tom does not sing, Sally dances
  • 4.If Sally does not dance, then Tom does not sing ✓
9.Which of the following is a form of modus tollens?
  • 1.If P, then Q. Q is true. Therefore, P is true.
  • 2.If P, then Q. Q is false. Therefore, P is false. ✓
  • 3.If P, then Q. P is false. Therefore, Q is false.
  • 4.If P, then Q. Q is false. Therefore, P is false.

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10.Which logical expression represents the negation of "If it is sunny, we will go to the park"?
  • 1.It is not sunny, and we will not go to the park
  • 2.It is sunny, and we will not go to the park ✓
  • 3.If it is not sunny, we will go to the park
  • 4.We will go to the park, even if it is not sunny
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