Question Video: Finding a Relation on a Set given Its Rule | Nagwa Question Video: Finding a Relation on a Set given Its Rule | Nagwa

# Question Video: Finding a Relation on a Set given Its Rule Mathematics • Third Year of Preparatory School

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Set 𝑋 = {−9, −4, 0, 4, 9}. Determine the relation 𝑅 on 𝑋, where 𝑎 𝑅𝑏 means that the numbers 𝑎 and 𝑏 are additive inverses with 𝑎 ∈ 𝑋 and 𝑏 ∈ 𝑋.

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### 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.

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