(i) 1 1 is in S. (ii) If a b is in S, where a b is written in lowest terms (that is, a and b have highest common factor 1), then b 2a is in S. (iii) If a b and c d are in S, where they are written in lowest terms, then a+c b+d is in S.

The expression can be T(X) = X/3 + 1 where X is the number of students, and we always should round up our solution if it is not a whole number.

Step-by-step explanation:

She needs a tent for every 3 campers, and she also needs a tent for herself.

This means that if X is the number of campers, we need to have:

T(X) = X/3 + 1

this means that we divide X into groups of 3, and for each group of 3 we have one tent, plus one that we need for the camp leader.

now, if for example we have 10 campers, we will have:

T(10) = 10/3 + 1 = 3.33 + 1

So we will need to round up the number of tents to 4 + 1