[Verse 1] In mathematics we need a way To show how elements can relate Take a set called A, now here's the key We'll build relations systematically A binary relation R you see Is just a subset of A cross A When element a connects to b We write it as aRb [Chorus] Relations, relations, connecting the dots Ordered pairs in a subset, that's what we've got aRb means a relates to b Binary relations, the foundation key A cross A, pick and choose Which pairs follow the relation rules [Verse 2] Let's see some examples, make it clear Numbers and the "less than or equal" here Three relates to five because it's true Three is less than five, so we're through The ordered pair three comma five Lives in our relation set, alive In the integers this pattern flows Less than or equal, that's how it goes [Chorus] Relations, relations, connecting the dots Ordered pairs in a subset, that's what we've got aRb means a relates to b Binary relations, the foundation key A cross A, pick and choose Which pairs follow the relation rules [Verse 3] "Divides" relation on natural numbers Three divides twelve, no need to wonder Since twelve equals three times four This ordered pair is in our store Or think of people, family tree "Sibling of" relation, you and me If John's related to his sister Jane Then that pair's in our relation chain [Bridge] From A cross A we take a part That's how relations get their start Not every pair needs to belong Just those that make the relation strong [Chorus] Relations, relations, connecting the dots Ordered pairs in a subset, that's what we've got aRb means a relates to b Binary relations, the foundation key A cross A, pick and choose Which pairs follow the relation rules [Outro] Binary relations, now you know How mathematical connections grow From ordered pairs to patterns clear Relations make the structure here
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