Question

Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " A function is rational if it is a polynomial.

Short answer

The sentence in 'If P, then Q' form is 'If it is a polynomial, then a function is rational'.

Step-by-step solution

Identify the Conditional Clause (P)

In the given sentence, 'it is a polynomial' is presented as the condition. This is because the sentence says a function is rational if this condition is met. So, P is 'It is a polynomial'.

Identify the Consequent Clause (Q)

In the given sentence, 'a function is rational' is the consequence of the condition being true. So, Q is 'A function is rational'.

Formulate the 'If P, then Q' sentence

Now that we have identified P and Q, we can put them together to form the sentence in 'If P, then Q' form. P goes after 'if' and Q goes after 'then'.