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What is logically equivalent to the following statements? "I pass only if you pass" (Note that fail is equivalent to not pass.)
  • a)
    You pass only if I pass
  • b)
    If you fail then I fail
  • c)
    If you pass then I pass
  • d)
    You fail if I pass.
Correct answer is option 'B'. Can you explain this answer?
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What is logically equivalent to the following statements? "I pass...
Without knowing the specific statements, it is not possible to determine what is logically equivalent to them. Please provide the statements you are referring to.
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What is logically equivalent to the following statements? "I pass...
Concept:
Logically Equivalent: Two expressions are logically equivalent provided that they have the same truth value for all possible combinations of truth values for all variables appearing in the two expressions. In this case, we write X≡Y and say that X and Y are logically equivalent.

The given expression is,
 "I pass only if you pass"
P = I pass.
¬P = I fail.
Q = you pass.
¬Q = you fail.
 "I pass only if you pass" = P ⇒ Q = ¬P ∨ Q
Option 1: You pass only if I pass
False,  Q ⇒ P = ¬Q ∨ P
Option 2: If you fail then I fail
True, ¬Q ⇒ ¬P = Q∨ ¬P
Option 3: If you pass then I pass.
False, Q ⇒ P = ¬Q ∨ P
Option 4: You fail if I pass.
False, ¬Q ⇒ P = Q ∨ P
Hence the correct answer is If you fail then I fail.
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What is logically equivalent to the following statements? "I pass only if you pass" (Note that fail is equivalent to not pass.)a)You pass only if I passb)If you fail then I failc)If you pass then I passd)You fail if I pass.Correct answer is option 'B'. Can you explain this answer?
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