Given a relation "R" and "a R b"; if "b R a" is true for all a and b, then the relation R is said to by symmetric.

STATEMENT: Given the relation of "equality" (=), and a = b; if b = a is true for all a and b, then equality is said to be symmetric.

Examples

• Since 2 + 3 = 5, then 5 = 2 + 3
• Since (2)(3) = 6, then 6 = (2)(3)
• Since 2x + 3 = 11, then 11 = 2x + 3
• Since 2x + 3x = 5x, then 5x = 2x + 3x

The statement is TRUE for all a and b (no counterexample can be found).

This is called the symmetric property of equality.

STATEMENT: Given the relation "is less than" (<), and a < b; if b < a is true for all a and b, then "is less than" is said to be symmetric.

Example: Given 1 < 2, it is NOT true that 2 < 1.

Since a counterexample can be found, the statement is NOT true for all a and b.

As a result, the relation "is less than" is NOT symmetric.