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.

To express the statement "Every comedian is funny" using logical notation, we can follow these steps:

1. ### Break Down the Problem

The statement asserts a universal condition about all comedians and their quality of being funny. We need to convert this into a logical expression using predicates and quantifiers.

2. ### Relevant Concepts

In predicate logic:

• The universal quantifier, denoted by $\forall$, indicates that the statement applies to all elements in the domain.
• The predicates given are:
  • $C(x)$: "x is a comedian"
  • $F(x)$: "x is funny"

3. ### Analysis and Detail

We want to convey that if someone is a comedian, they are funny. This leads to the expression: $\forall x (C(x) \rightarrow F(x))$ Here, $\rightarrow$ stands for implication, meaning "if C(x) holds true, then F(x) will also hold true."

4. ### Verify and Summarize

The statement correctly captures that for every person $x$ in the domain (all people), if $x$ is a comedian, then $x$ is also funny. This logical formulation encompasses all members of the domain and adequately represents the given statement.

Final Answer

The logical representation of "Every comedian is funny" is: $\forall x (C(x) \rightarrow F(x))$