Question

Negate the following sentences. The number \(x\) is positive, but the number \(y\) is not positive.

Short answer

The negated sentence of 'The number \(x\) is positive, but the number \(y\) is not positive.' is 'The number \(x\) is not positive and the number \(y\) is positive.'

Step-by-step solution

Identify the Statements

The sentence provided contains two distinct parts: 'The number \(x\) is positive' and 'The number \(y\) is not positive'. Negate each part separately.

Negate Statement 1

Our first statement is 'The number \(x\) is positive'. To negate this, we say 'The number \(x\) is not positive' (or 'The number \(x\) is negative or zero').

Negate Statement 2

Our second statement is 'The number \(y\) is not positive'. To negate this, we set aside the not and say 'The number \(y\) is positive'.

Combine the negated statements

We combined the two negated statements using 'and' as follows: 'The number \(x\) is not positive and the number \(y\) is positive'