Question

Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " For a function to be continuous, it is sufficient that it is differentiable.

Short answer

The given sentence converted in 'If-Then' form is: 'If a function is differentiable, then it is continuous.'

Step-by-step solution

Identify the 'P' and 'Q' Statements

The task is to convert the statement 'For a function to be continuous, it is sufficient that it is differentiable.' into 'if-then' format. Here, 'A function being continuous' can be considered as the result or 'Q' and 'it being differentiable' is considered as the condition or 'P'.

Formulate the 'If-Then' Statement

Using the identified 'P' and 'Q' statements from the first step, formulate the sentence in 'If-then' format. So, the statement becomes 'If a function is differentiable, then it is continuous.'