Anonymous asked in Science & MathematicsMathematics · 7 months ago

Relations definition help - don't understand?

So I'm learning about relations in class but I don't really understand the example in the slide below. Like why is R={(1,1), (1,2), (1,3), (2,2), (3,3)}? Where did those values come from?

What is (a,b) supposed to represent?

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2 Answers

  • 7 months ago
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    Oh hey look google is there!

    The way we frequently describe a relation in writing is using a set of ordered pairs (x,y).

    The example was clearly written in a caffeine induced frenzy since they really did not say what a and b are.

    a and b are obviously supposed to be any two numbers from the set A.

    Since 1 divides 1, then (1, 1) is a pair that obeys the relation so you put it in R.

    Since 1 divides 2, then (1, 2) is also such a pair.

    Obviously order is important. 2 does not divide 1 hence (2, 1) is not an appropriate pair - we say the relation is not "symmetric".

    A relation such as T = { (a,b) | a^2 = b^2 } is symmetric because obviously if a pair (a, b) obeys the relation then so does (b, a)

    (-1)^2 = 1^2 and 1^2 = (-1)^2

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  • 7 months ago

    The values in the pairs of R come from the definition of the relation as: {(a,b) | a divides b}. (1,2) is in the relation R since the a value (1) evenly divides the b value (2). (Remember that "a divides b" means that integer division of (b) by (a) has a remainder of zero.) The pair (2,3) is not in the relation because 2 does not divide 3.

    The numbers in A = {1, 2, 3} are simply made up; but you probably figured that out. :^)

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