What is the algebraic property demonstrated by if x = 3 and 3 = y, then x = y?

Solution:

Given that : If x = 3 and 3 = y, then x = y.

This demonstrates ‘transitive property’ which states that, for all real numbers x, y, z, if x = y and y = z then x =z.

The transitive property of equality is one of the equivalence properties of equality and inequality. The algebraic transitive property is extended to geometrical shapes too as transitive property of congruence.

This property can also be observed in a set of parallel straight lines in a plane. That is, if line 1 (say l₁) is parallel to line 2 (say l₂) and l₂ is parallel to line 3 (say l₃) then, line one l₁ is parallel to line l₃.

What is the algebraic property demonstrated by if x = 3 and 3 = y, then x = y?

Summary:

Given x = 3 and 3 = y, then x = y, demonstrates the ‘transitive property’.