Question

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. $$ \begin{array}{ll}{\text { a) } \forall x(C(x) \rightarrow F(x))} & {\text { b) } \forall x(C(x) \wedge F(x))} \\ {\text { c) } \quad \exists x(C(x) \rightarrow F(x))} & {\text { d) } \exists x(C(x) \wedge F(x))}\end{array} $$

Name: Problem 7, Chapter 1: Discrete Mathematics and its Applications
Uploaded: 2021-08-22T19:55:55-08:00
Duration: 1 min 26 s
Channel: Christopher Stanley
Description: 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))

   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.
$$
\begin{array}{ll}{\text { a) } \forall x(C(x) \rightarrow F(x))} & {\text { b) } \forall x(C(x) \wedge F(x))} \\ {\text { c) } \quad \exists x(C(x) \rightarrow F(x))} & {\text { d) } \exists x(C(x) \wedge F(x))}\end{array}
$$

Discrete Mathematics and its Applications

Kenneth Rosen 8th Edition

Chapter 1, Problem 7

Instant Answer

Solved by Expert Christopher Stanley

08/22/2021

Step 1

The symbol $\forall$ means "for all", $C(x)$ means "$x$ is a comedian", $\rightarrow$ means "implies", and $F(x)$ means "$x$ is funny". So, this statement translates to "For every person, if they are a comedian, then they are funny". Show more…

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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. $$ \begin{array}{ll}{\text { a) } \forall x(C(x) \rightarrow F(x))} & {\text { b) } \forall x(C(x) \wedge F(x))} \\ {\text { c) } \quad \exists x(C(x) \rightarrow F(x))} & {\text { d) } \exists x(C(x) \wedge F(x))}\end{array} $$

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Key Concepts

Logical Implication

Logical implication (?) represents a conditional statement where if the antecedent is true, then the consequent must also be true. In translations, it is read as 'if... then,' establishing a dependency between two properties.

Logical Conjunction

Logical conjunction (?) combines two statements, requiring both to be true simultaneously. It is commonly translated as 'and,' indicating that both conditions or properties must hold together.

Universal Quantifier

The universal quantifier (?) expresses that a statement applies to every element in the domain. In logic, it is used to assert that every person or object under consideration satisfies a given property or relation.

Existential Quantifier

The existential quantifier (?) indicates that there is at least one element in the domain for which the statement holds. It is used to assert the existence of some person or object that satisfies the given conditions.

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