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¬ (p ↔ q) is logically equivalent to
- a)p ↔ ¬q
- b)¬p ↔ q
- c)¬p ↔ ¬q
- d)¬q ↔ ¬p
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
¬ (p ↔ q) is logically equivalent toa)p ↔ ¬qb)¬p...
Explanation:
- Logical Equivalence:
- When two statements have the same truth values in all possible scenarios, they are said to be logically equivalent. In this case, we are looking to identify the logical equivalence of the statement ¬(p ↔ q).
- Using Logical Equivalence Laws:
- To determine the logical equivalence of ¬(p ↔ q), we can use the logical equivalence laws to simplify the expression.
- The logical equivalence law for the biconditional statement (p ↔ q) is ¬p ↔ q.
- Applying the negation law, we get ¬(p ↔ q) ≡ p ↔ ¬q.
- Choosing the Correct Option:
- From the given options, the statement p ↔ ¬q matches with our simplified expression of ¬(p ↔ q).
- Therefore, the correct answer is option 'A', which states that p ↔ ¬q is logically equivalent to ¬(p ↔ q).
By applying logical equivalence laws and simplifying the given expression, we have determined that option 'A' is the correct choice as it represents the logical equivalence of the given statement.
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Community Answer
¬ (p ↔ q) is logically equivalent toa)p ↔ ¬qb)¬p...
(¬ (p ↔ q)) ↔ (p ↔ ¬q) is tautology.
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¬ (p ↔ q) is logically equivalent toa)p ↔ ¬qb)¬p ↔ qc)¬p ↔ ¬qd)¬q ↔ ¬pCorrect answer is option 'A'. Can you explain this answer?
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