Let’s do part b). Start with an element is the composition.
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Using the definitions of the two relations we get:
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Putting those together we see that or .
Thus the answer is .
Can someon show me how to do one of these problems step by step so I have an idea of how to work these problems. I do not know what to do.
R1 = {(a, b) R^2 | a > b}, the "greater than" relation
R2 = {(a, b) R^2 | a > b}, the "greater than or equal to" relation
R3 = {(a, b) R^2 | a < b}, the "less than" relation
R4 = {(a, b) R^2 | a < b}, the "less than or equal to" relation
R5 = {(a, b) R^2 | a = b}, the "equal to" relation
R6 = {(a, b) R^2 | a b}, the "equal to" relation
Find:
a.) R1 o R1
b.) R1 o R2
c.) R1 o R3
d.) R1 o R4
e.) R1 o R5
f.) R1 o R6
g.) R2 0 R3
h.) R3 o R3
Composition of relations has very little in common with union, intersection, etc of relations.
Those are just ordinary set operations: membership of pairs.
Whereas, composition of relations (leads to composition of functions) has to do with the existence of two particular pairs implying the existence of a third pair.
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Notice that the definition is ‘if and only if’.
Also we work from right to left in the composition, start with the and then the .