which of the following relations are odd?
I. y=2
II. y=x
III. x^2 + y^2 = 1
A) only II
B) only I and II
c) only I and III
D) only II and III
E) I,II and III

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Solution

$U s e t h e a p p r o p r i a t e t e s t f o r d e t e r m i n i n g w h e t h e r t h e r e a l t i o n i o s o d d o r e v e n I . T h e g r a p h o f y = 2 i s a h o r i z o n t a l l i n e, w h i c h i s n o t s y m m e t r i c a b o u t t h e o r i g i n, s o y = 2 i s n o t o d d . I I . S i n c e f (- x) = - x = - f (x), t h i s f u n c t i o n i s o d d . I I I . S i n c e (- x)^{2} + (y)^{2} = 1 w h e n e v e r x^{2} + y^{2} = 1 d o e s, t h i s r e l a t i o n i s o d d . S o, o n l y I I a n d I I I r e l a t i o n s a r e o d d$

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