Question

euclid relied on five basic axioms to build the propositions in his book elements. the first axiom states, \things that are equal to the same thing are also equal to one another.\ which modern mathematical statement is equivalent to this axiom? if a = b, then b = a. if a = b and b = c, then a = c. if a ≠ b, then b ≠ a. if a = b, then a + c = b + c.

Explanation:

Euclid's first axiom means if two things are equal to a third thing, they are equal to each other. The statement "If \(a = b\) and \(b = c\), then \(a=c\)" represents the transitive - property of equality which is equivalent to the given axiom. The first option is the symmetric property, the third is a non - equality statement, and the fourth is the addition property of equality.

Answer:

If \(a = b\) and \(b = c\), then \(a = c\).