Question

state the relation that are not equivalence

Answer 1

Now that we have a formal way to define an equivalence relation, let's go back to our initial three attempts to define equivalence and see which one is not an equivalence relation.

Example One: Are Raspberries Equivalent to Strawberries?

Consider our first relation, 'having the same color', with the set we're considering being the set of all berries. First, we'll check if the relation is reflexive. Does a berry have the same color as itself? Yeah, that seems right. Good! This relation is reflexive.

Next, we'll check if the relation is symmetric. If one berry has the same color as another berry, does this second berry have the same color as the first berry? Again, that seems pretty obvious. Great! The relation is symmetric