10 grade maths> Let R = {(a, a)} be a relation on set A. ...
Let R = {(a, a)} be a relation on set A. then R is
1 AnswersTo analyze the relation R = {(a, a)} on set A, we need to understand the definitions of symmetric and antisymmetric relations.
A relation R is symmetric if, for every pair (x, y) in R, the pair (y, x) is also in R. In this case, since R contains only the pair (a, a), we have:
This means R is symmetric.
A relation R is antisymmetric if, for every pair (x, y) in R, whenever (x, y) and (y, x) are both in R, then x must equal y. Here, we only have the pair (a, a), which satisfies this condition because:
Given that R is both symmetric and antisymmetric, the correct answer is:
3) Symmetric and antisymmetric
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