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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"?

  • أIf the ground does not get wet, it does not rain
  • بIf it rains, the ground will not get wet
  • تIf the ground gets wet, it rains
  • 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.

  • أAll animals are cats
  • بSome animals are not cats
  • تNo cats are animals
  • All cats are animals
3

In the statement "Either Tom or Jerry will win the race," which logical operation is primarily used?

  • أConjunction
  • بNegation
  • تImplication
  • Disjunction
4

What is the contrapositive of the statement "If the sky is overcast, then it will rain"?

  • أIf it does not rain, the sky is not overcast
  • بIf the sky is not overcast, it will rain
  • تIf it rains, the sky is not overcast
  • If it does not rain, then the sky is not overcast
5

Which of the following statements is an example of a tautology?

  • أThe apple is red or it is not red
  • بThe cat is on the mat and it is not raining
  • تIf I win the lottery, I will be happy
  • It is raining or it is not raining
6

If "All A are B" and "Some B are C," which conclusion cannot be correctly inferred?

  • أSome A are C
  • بSome C are A
  • تAll C are A
  • Some B are A
7

Which operation shows the logical equivalence in "p AND q"?

  • أq AND p
  • NOT (p OR q)
  • تp OR NOT q
  • ثNOT p AND q
8

From the premise "If Sally dances, then Tom sings," which is the inverse?

  • أIf Sally does not dance, Tom sings
  • بIf Tom sings, Sally dances
  • تIf Tom does not sing, Sally dances
  • If Sally does not dance, then Tom does not sing
9

Which of the following is a form of modus tollens?

  • أIf P, then Q. Q is true. Therefore, P is true.
  • If P, then Q. Q is false. Therefore, P is false.
  • تIf P, then Q. P is false. Therefore, Q is false.
  • ثIf P, then Q. Q is false. Therefore, P is false.
10

Which logical expression represents the negation of "If it is sunny, we will go to the park"?

  • أIt is not sunny, and we will not go to the park
  • It is sunny, and we will not go to the park
  • تIf it is not sunny, we will go to the park
  • ثWe will go to the park, even if it is not sunny