Question

Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?" transitive reflexive symmetric

Answer 1

Answer: Transitive property.

Explanation:

First, for the equality we have:

Reflexive:

For all real numbers x, x = x.

Symmetric:

For all real numbers x, y

if x= y, then y = x.

Transitive:

For reals x, y and z.

if x = y, and y = z, then x = z.

Now, let's talk about inequalities.

first, the reflexive property will say that:

x > x.

This has no sense, so this property does not work for inequalities.

Now, the reflexive.

If x > y, then y > x.

Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.

Not, the transitive property.

if x > y, and y > z, then x > z.

This is true.

x is bigger than y, and y is bigger than z, then x should also be bigger than z.

x > y > z.

And this also works for the inverse case:

x < y and y < z, then x < z.

So the correct option is transitive property.