1Suppose S is a set people and R is the following relation o

1.Suppose S is a set people, and R is the following relation on S: aRb if and only if a has chatted with b on the internet. Explain your answers to the following questions and use common sense.

What is the meaning of the relation R2 ? Specifically, when are two people R2 related?

2. Suppose S is a set of integers, and R is the following relation on S: aRb if and only if a < b. Explain your answers to the following questions.

What is the meaning of the relation R2 ? Specifically, when are two integers R2 related?

Solution

2.

For this question What is the meaning of the relation R2 ? Specifically, when are two integers R2 related?

The composition of relations works as follows: if R and Q are two relations over the same set which is S- Set of inetegers, then x(QR)z if and only if there exists y such that xRy and yQz, that is in general terms we say that, a < c in QR if and only if a < b (in R) and b < c (in Q). So in our case, x(R^2)z if and only if there exists some b in y such that a < c where b exists in betwee so that a < b and b < c.

1.

Can be solved using same principle as above