# Translating Quantified Statements Into English

• Bashyboy
In summary, the given statements are translated into English using the domain of all people and the predicates C(x) and F(x) for "x is a comedian" and "x is funny" respectively. The solutions are as follows: a) For every person, if they are a comedian, then they are funny. b) For every person, they are both a comedian and funny. c) There exists a person who, if they are funny, is a comedian. d) There exists a person who is funny and is a comedian. The solution manual provides the following answers: a) Every comedian is funny. b) Every person is a funny comedian. c) There exists a person such that
Bashyboy

## Homework Statement

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))

## The Attempt at a Solution

For a): For every person, if they are a comedian, then they are funny.

For b): For every person, they are both a comedian and funny.

For c): There exists a person who, if he is funny, is a comedian

For d): There exists a person who is funny and is a comedian.

a)Every comedian is funny.
b)Every person is a funny comedian.
c)There exists a person such that if she or he is a comedian, then she or he is funny.
d)Some comedians are funny.

Does the meaning of my answers seem to be in harmony with the meaning of the answers given in the solution manual?

The reason I ask is because part a), for instance, is a implication, and "Every comedian is funny," does not appear to be an implication.

## 1. What is the purpose of translating quantified statements into English?

The purpose of translating quantified statements into English is to make them easier to understand and interpret. Quantified statements, also known as logical statements, are often written in mathematical or symbolic notation, which can be confusing for those who are not familiar with them. Translating them into English allows for a clearer and more concise representation of the logical relationships being expressed.

## 2. How do you translate a universal quantified statement into English?

A universal quantified statement is one that applies to all elements in a given set or domain. To translate this into English, you would use the phrase "for all" or "for every" followed by the subject and predicate of the statement. For example, the statement "∀x (x is a mammal)" can be translated as "For every x, x is a mammal." This indicates that every element in the set being considered is a mammal.

## 3. How do you translate an existential quantified statement into English?

An existential quantified statement is one that asserts the existence of at least one element in a given set or domain. To translate this into English, you would use the phrase "there exists" followed by the subject and predicate of the statement. For example, the statement "∃x (x is a prime number)" can be translated as "There exists an x such that x is a prime number." This indicates that at least one element in the set being considered is a prime number.

## 4. What does it mean to translate a quantified statement into English with a conditional?

Translating a quantified statement into English with a conditional means that the statement includes an "if-then" structure. For example, the statement "∀x (x is a mammal → x has fur)" can be translated as "For every x, if x is a mammal, then x has fur." This indicates that if an element is a mammal, then it must have fur.

## 5. Are there any common errors to avoid when translating quantified statements into English?

One common error to avoid when translating quantified statements into English is using vague or ambiguous language. It is important to use precise and specific language when translating these statements to avoid misinterpretation. Additionally, be careful not to change the meaning of the statement when translating it into English, as this can lead to incorrect conclusions.

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