### Video Transcript

Set 𝑋 contains the numbers
negative nine, negative four, zero, four, and nine. Determine the relation 𝑅 on 𝑋,
where 𝑎𝑅𝑏 means that the numbers 𝑎 and 𝑏 are additive inverses with 𝑎 an
element of 𝑋 and 𝑏 is an element of 𝑋.

We recall that a relation is a
collection of ordered pairs 𝑎, 𝑏. In this question, both 𝑎 and 𝑏
are contained in set 𝑋, the numbers negative nine, negative four, zero, four, and
nine. Two numbers are said to be the
additive inverse of each other if they sum to zero. One such pair in set 𝑋 is negative
nine and nine. Negative four plus four is also
equal to zero. Our third pair is zero, zero as
zero plus zero is equal to zero. We can also reverse the order of
our first two pairs. Four plus negative four and nine
plus negative nine are also equal to zero.

The relation 𝑅, therefore,
consists of the five ordered pairs negative nine, nine; negative four, four; zero,
zero; four, negative four; and nine, negative nine.