Question

Translate each of the following sentences into symbolic logic. If \(f\) is a polynomial and its degree is greater than 2 , then \(f^{\prime}\) is not constant.

Short answer

The symbolic logic translation of the sentence `If the function f is a polynomial and its degree is greater than 2 then f prime is not constant` is `(P ^ Q) -> R`

Step-by-step solution

Identify Propositions

First, identify the propositions in the sentence. A proposition is a statement that is either true or false. The propositions in this sentence are: `f is a polynomial`, `the degree of f is greater than 2`, and `f prime is not constant`.

Assign Symbols to Propositions

Next, assign symbols to these propositions. For example, one could use 'P' to represent `f is a polynomial`, 'Q' to represent `the degree of f is greater than 2`, and 'R' to represent `f prime is not constant`.

Identify Logical Connectives

Determine the logical connectives in the sentence, these are words like 'and', 'or', 'if...then...'. In this sentence, 'and' is a logical connective. In propositional logic, 'and' is usually represented by the symbol '^' and 'if...then...' is represented by '->'.

Form the Symbolic Logic Statement

Finally, form the symbolic logic statement based on the identified propositions and logical connectives. The sentence `If the function f is a polynomial and its degree is greater than 2 then f prime is not constant` would be translated as `(P ^ Q) -> R`, where parentheses indicate the order of operations.