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The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.
- a)∀x (F (x) → P (x))
- b)∀x (F (x) ∧ P (x))
- c)∃x (F (x) ∧ P (x))
- d)∃x (F (x) → P (x))
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The statement, “At least one of your friends is perfect”. ...
Understanding the Statement
The statement "At least one of your friends is perfect" implies that there exists at least one person within the set of your friends who is considered perfect.
Translation of the Statement
- Let P(x) represent "x is perfect."
- Let F(x) represent "x is your friend."
- The domain is all people.
Logical Interpretation of Options
- a) ∀x (F(x) → P(x)): This means every friend is perfect, which is too strong for the statement.
- b) ∀x (F(x) ∧ P(x)): This suggests all friends are perfect, which again does not align with the original statement.
- c) ∃x (F(x) ∧ P(x)): This indicates that there exists at least one person who is both a friend and perfect. This aligns perfectly with the original statement.
- d) ∃x (F(x) → P(x)): This suggests that there exists at least one person such that if they are a friend, then they are perfect. This does not guarantee that any friend is perfect.
Correct Answer Explanation
The correct answer is option c:
- It captures the essence of the statement, confirming that there is at least one friend who is perfect.
- This is a direct match to the meaning of "at least one," making it the most accurate representation of the original statement.
Conclusion
Understanding logical statements often requires careful consideration of the quantifiers and the relationships between the predicates. In this case, option c effectively conveys the intended meaning of the original statement.
The statement "At least one of your friends is perfect" implies that there exists at least one person within the set of your friends who is considered perfect.
Translation of the Statement
- Let P(x) represent "x is perfect."
- Let F(x) represent "x is your friend."
- The domain is all people.
Logical Interpretation of Options
- a) ∀x (F(x) → P(x)): This means every friend is perfect, which is too strong for the statement.
- b) ∀x (F(x) ∧ P(x)): This suggests all friends are perfect, which again does not align with the original statement.
- c) ∃x (F(x) ∧ P(x)): This indicates that there exists at least one person who is both a friend and perfect. This aligns perfectly with the original statement.
- d) ∃x (F(x) → P(x)): This suggests that there exists at least one person such that if they are a friend, then they are perfect. This does not guarantee that any friend is perfect.
Correct Answer Explanation
The correct answer is option c:
- It captures the essence of the statement, confirming that there is at least one friend who is perfect.
- This is a direct match to the meaning of "at least one," making it the most accurate representation of the original statement.
Conclusion
Understanding logical statements often requires careful consideration of the quantifiers and the relationships between the predicates. In this case, option c effectively conveys the intended meaning of the original statement.
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The statement, “At least one of your friends is perfect”. ...
Clarification: For some x, x is friend and funny.
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The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.a)∀x (F (x) → P (x))b)∀x (F (x) ∧ P (x))c)∃x (F (x) ∧ P (x))d)∃x (F (x) → P (x))Correct answer is option 'C'. Can you explain this answer?
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The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.a)∀x (F (x) → P (x))b)∀x (F (x) ∧ P (x))c)∃x (F (x) ∧ P (x))d)∃x (F (x) → P (x))Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.a)∀x (F (x) → P (x))b)∀x (F (x) ∧ P (x))c)∃x (F (x) ∧ P (x))d)∃x (F (x) → P (x))Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.a)∀x (F (x) → P (x))b)∀x (F (x) ∧ P (x))c)∃x (F (x) ∧ P (x))d)∃x (F (x) → P (x))Correct answer is option 'C'. Can you explain this answer?.
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