Translate these statements into English, where C(x) is “x is a comedian” and F(x) is “x is funny” and the domain consists of all people. a) ∀x(C(x) → F(x)) b) ∀x(C(x) ∧ F(x)) c) ∃x(C(x) → F(x)) d) ∃x(C(x) ∧ F(x))

Solution:

Let us translate the following statements into English sentence, where

$C(x)$ is "$x$ is a comedian" and $F(x)$ is "$x$ is funny" and the domain consist of all people.

a) $\forall x(C(x) \to F(x))$

If a human is a comedian then this human is a funny.

b) $∀x(C(x) ∧ F(x))$

A human is a comedian and funny.

c) $\exists x(C(x) \land F(x))$

There exists a human that is a comedian and a funny.

d) $\exists x(C(x) \to F(x))$

There exists a human such that If this human is a comedian then this human is a funny.