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Re: APCALC digest 393
Posted:
Sep 18, 1998 12:04 AM


In a message dated 980917 16:03:39 EDT, Mary Harrison wrote:
<< Topic of conversation in the math office today: Is it possible for a function or relation to be both symmetric to the y axis and to the origin but not to the xaxis? The only thing I could think of was 3/4 of a circle. Anything else? Other than variations of this (e.g. triangle segments) >> 3/4 circle is not symmetric to the origin!! The answer to the question is "NO." If the relation R is symmetric wrt y axis and origin, and (x, y) is an element of R, then (x, y) is an element of R as is (x, y). Then, since (x, y) is an element of R, (x, y)  the reflection of (x, y) wrt the origin  is also an element of R. So (x, y) element of R implies (x, y) is an element of R, and R is also symmetric wrt x axis!!
Martha Gregg Waverly, NE



