he statement,” Every comedian is funny” where C(x) is “x is a comedian” and F (x) is “x is funny” and the domain consists of all people.
Question
The statement,
"Every comedian is funny"
where
- C(x) is "x is a comedian"
- F(x) is "x is funny"
- the domain consists of all people.
Solution
The statement "Every comedian is funny" can be translated into logical form as follows:
∀x (C(x) → F(x))
This reads as "For all x, if x is a comedian then x is funny". This is under the assumption that the domain consists of all people.
Here's the step by step breakdown:
-
∀x: This symbol represents "for all" or "for every". In this case, it means "for every person x".
-
C(x): This is a predicate that represents "x is a comedian".
-
→: This symbol represents "implies" or "then". It's used to connect the condition (x is a comedian) to the result (x is funny).
-
F(x): This is a predicate that represents "x is funny".
So, putting it all together, ∀x (C(x) → F(x)) means "For every person x, if x is a comedian, then x is funny". This is the logical form of the statement "Every comedian is funny".
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