2
Question
The given diagram shows a relation from A to B. Denoting the elements of A by x and those of B by y, the relation between them is given by
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Solution
x=−2⟹y=−2 and y=2
x=0⟹y=0
x=3⟹y=3 and y=−3
x=7⟹y=7 and y=−7
Each x value has two y values, where one value is x and the other is −x.
Thus, the relation is given by:
y=±x
x=−2⟹y=−2 and y=2
x=0⟹y=0
x=3⟹y=3 and y=−3
x=7⟹y=7 and y=−7
Each x value has two y values, where one value is x and the other is −x.
Thus, the relation is given by:
y=±x
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, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.