The 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.ans.∃x(C(x) ∧ F (x))∀x(C(x) → F (x))∃x(C(x) → F (x))∀x(C(x) ∧ F (x))
Question
The 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.ans.∃x(C(x) ∧ F (x))∀x(C(x) → F (x))∃x(C(x) → F (x))∀x(C(x) ∧ F (x))
Solution
The statement "Every comedian is funny" can be translated into predicate logic as follows:
∀x(C(x) → F (x))
This statement is read as "For all x, if x is a comedian then x is funny". This is the correct translation of the statement because it captures the idea that every person who is a comedian is also funny.
The other options are not correct translations of the statement:
∃x(C(x) ∧ F (x)) is read as "There exists an x such that x is a comedian and x is funny". This statement only asserts that there is at least one person who is both a comedian and funny, not that every comedian is funny.
∃x(C(x) → F (x)) is read as "There exists an x such that if x is a comedian then x is funny". This statement only asserts that there is at least one person who, if they are a comedian, is also funny. It does not assert that every comedian is funny.
∀x(C(x) ∧ F (x)) is read as "For all x, x is a comedian and x is funny". This statement asserts that every person is both a comedian and funny, which is not what the original statement says.
Similar Questions
The 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.ans.
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s this ∃xQ(x) a tautology
Universal Quantifier
Suppose f(x) =1𝑥x1 then (𝑓∘𝑓∘𝑓)(𝑥)(f∘f∘f)(x) =A.11𝑥x1 1 B.1𝑥x1 C.𝑥2x 2 D.1𝑥2x 2 1 E.xSUBMITarrow_backPREVIOUS
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