Question

Let p: A number is greater than 25. Let q: A number is less than 35. If p ∧ q is true, then what could the number be?

Answer 1

Answer: Any number between 25 and 35 excluding both endpoints

(ie the number cannot be 25, the number cannot be 35)

One possible answer is 27 but there are infinitely many other choices

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Explanation:

The notation p ^ q in a logic math class setting means "p and q". Basically its a way of saying "both p and q are the case of some event happening". More specifically, it means that we have some number that is greater than 25 AND it is also less than 35.

If x is that number then p translates to x > 25. Statement q translates to x < 35

Flip both sides of x > 25 to get 25 < x.

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So we have 25 < x  and x < 35. Those two combine to 25 < x < 35

Therefore x is some number between 25 and 35, where we leave out both endpoints. You can pick any number from this interval.