In 34-36, assume that R is a relation on a et A. Prove or disprove each statement.

If R is transitive, then R − 1 is transitive.

To prove that if R is transitive, then R−1 is transitive.

Given information:

Assume that R is a relation on a set A and R is transitive.

Proof:

Let us assume that R is transitive and let (a,b)∈R−1 and let (b,c)∈R−1.

By the definition of the inverse relation:

(a,b)∈R−1⇒(b,a)∈R(b,c)∈R−1⇒(c,b)∈R

By the definition of transitive (since R is transitive):

(b,a)∈R and (c