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In propositional logic P ↔ Q is equivalent to (Where ~ denotes NOT):
- a)~( P ∨ Q ) ∧ ~ ( Q ∨ P )
- b)( ~P ∨ Q ) ∧ (~ Q ∨ P )
- c)( P ∨ Q ) ∧ ( Q ∨ P )
- d)~( P ∨ Q ) → ~ ( Q ∨ P )
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In propositional logic P ↔ Q is equivalent to (Where ~ denotes NO...
P ↔ Q = (P → Q) ∧ (Q → P)
P ↔ Q = (~P ∨ Q) ∧ (~Q v P)
So, option (B) is correct.
P ↔ Q = (~P ∨ Q) ∧ (~Q v P)
So, option (B) is correct.
Most Upvoted Answer
In propositional logic P ↔ Q is equivalent to (Where ~ denotes NO...
Explanation:
Understanding the Equivalence:
- The expression P ↔ Q represents the biconditional logical operator, which means "P if and only if Q". It is true when both P and Q have the same truth values.
- To determine the equivalence of P ↔ Q, we need to simplify the expression and check if it is equivalent to the given options.
Breaking Down the Equivalence:
- The given option ( ~P ∨ Q ) ∧ (~ Q ∨ P ) can be simplified using De Morgan's laws and the commutative property of logical operators.
- ~P ∨ Q is equivalent to ~(P ∧ ~Q) by De Morgan's law.
- Similarly, ~Q ∨ P is equivalent to ~(Q ∧ ~P).
- Combining both expressions, we get ~(P ∧ ~Q) ∧ ~(Q ∧ ~P), which simplifies to ~(P ↔ Q).
Conclusion:
- Therefore, the expression ~(P ↔ Q) is equivalent to the given option ( ~P ∨ Q ) ∧ (~ Q ∨ P ), making option 'B' the correct answer.
Understanding the Equivalence:
- The expression P ↔ Q represents the biconditional logical operator, which means "P if and only if Q". It is true when both P and Q have the same truth values.
- To determine the equivalence of P ↔ Q, we need to simplify the expression and check if it is equivalent to the given options.
Breaking Down the Equivalence:
- The given option ( ~P ∨ Q ) ∧ (~ Q ∨ P ) can be simplified using De Morgan's laws and the commutative property of logical operators.
- ~P ∨ Q is equivalent to ~(P ∧ ~Q) by De Morgan's law.
- Similarly, ~Q ∨ P is equivalent to ~(Q ∧ ~P).
- Combining both expressions, we get ~(P ∧ ~Q) ∧ ~(Q ∧ ~P), which simplifies to ~(P ↔ Q).
Conclusion:
- Therefore, the expression ~(P ↔ Q) is equivalent to the given option ( ~P ∨ Q ) ∧ (~ Q ∨ P ), making option 'B' the correct answer.
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In propositional logic P ↔ Q is equivalent to (Where ~ denotes NOT):a)~( P ∨ Q ) ∧ ~ ( Q ∨ P )b)( ~P ∨ Q ) ∧ (~ Q ∨ P )c)( P ∨ Q ) ∧ ( Q ∨ P )d)~( P ∨ Q ) → ~ ( Q ∨ P )Correct answer is option 'B'. Can you explain this answer?
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In propositional logic P ↔ Q is equivalent to (Where ~ denotes NOT):a)~( P ∨ Q ) ∧ ~ ( Q ∨ P )b)( ~P ∨ Q ) ∧ (~ Q ∨ P )c)( P ∨ Q ) ∧ ( Q ∨ P )d)~( P ∨ Q ) → ~ ( Q ∨ P )Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about In propositional logic P ↔ Q is equivalent to (Where ~ denotes NOT):a)~( P ∨ Q ) ∧ ~ ( Q ∨ P )b)( ~P ∨ Q ) ∧ (~ Q ∨ P )c)( P ∨ Q ) ∧ ( Q ∨ P )d)~( P ∨ Q ) → ~ ( Q ∨ P )Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In propositional logic P ↔ Q is equivalent to (Where ~ denotes NOT):a)~( P ∨ Q ) ∧ ~ ( Q ∨ P )b)( ~P ∨ Q ) ∧ (~ Q ∨ P )c)( P ∨ Q ) ∧ ( Q ∨ P )d)~( P ∨ Q ) → ~ ( Q ∨ P )Correct answer is option 'B'. Can you explain this answer?.
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