Question

Without changing their meanings, convert each of the following sentences into a sentence having the form "If \(P\), then \(Q .\) " Whenever a surface has only one side, it is non-orientable.

Short answer

The sentence 'Whenever a surface has only one side, it is non-orientable' can be changed without modifying its meaning into 'If a surface has only one side, then it is non-orientable'

Step-by-step solution

- Identify the condition 'P'

In the sentence 'Whenever a surface has only one side', 'a surface has only one side' is the condition, denoted as 'P'.

- Identify the result 'Q'

In the sentence 'it is non-orientable', 'it is non-orientable' is the consequence or outcome that results when the condition P is meet, denoted as 'Q'.

- Formulate into If-Then statement

Combine the identified P and Q into a sentence of the form 'If \(P\), then \(Q\)'. This should be 'If a surface has only one side, then it is non-orientable'