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

If R is symmetricm, then R − 1 is symmetric.

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

Given information:

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

Proof:

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

By the definition of the inverse relation:

(b,a)∈R

By the definition of symmetric relation:

(b,a)∈R⇒(a,b)∈R

By the definition of the inverse relation:

(a,b