1. Tardigrade
  2. Question
  3. Mathematics
  4. The graph of a relation is (i) Symmetric with respect to the x-axis provided that whenever (a, b) is a point on the graph, so is ( a ,- b ) (ii) Symmetric with respect to the y-axis provided that whenever (a, b) is a point on the graph, so is (- a , b ) (iii) Symmetric with respect to the origin provided that whenever (a, b) is a point on the graph, so is (- a ,- b ) (iv) Symmetric with respect to the line y = x, provided that whenever ( a , b ) is a point on the graph, so is (b, a) Suppose R is a relation whose graph is symmetric to both the x-axis and y-axis, and that the point (1, 2) is on the graph of R. Which one of the following points is NOT necessarily on the graph of R?

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Q. The graph of a relation is
(i) Symmetric with respect to the $x$-axis provided that whenever (a, b) is a point on the graph, so is $( a ,- b )$
(ii) Symmetric with respect to the $y$-axis provided that whenever $(a, b)$ is a point on the graph, so is $(- a , b )$
(iii) Symmetric with respect to the origin provided that whenever (a, b) is a point on the graph, so is $(- a ,- b )$
(iv) Symmetric with respect to the line $y = x$, provided that whenever $( a , b )$ is a point on the graph, so is $(b, a)$
Suppose R is a relation whose graph is symmetric to both the x-axis and y-axis, and that the point (1, 2) is on the graph of R. Which one of the following points is NOT necessarily on the graph of R?

Relations and Functions - Part 2

Solution:

Suppose $R$ is just a rectangle whose 4 vertices are $(1,2),(1,-2),(-1,2)$ and $(-1,-2)$. The $x$-axis and $y$-axis symmetries in the problem are satisfied, but the point $(2,1)$ is not contained in $R$.]