If `R` is a relation on the set `A={1,\ 2,\ 3}` given by `R=(1,\ 1),\ (2,\ 2),\ (3,\ 3)` , then `R` is (a) reflexive (b) symmetric (c) transitive (d) all the three options

Answer

d) all the three options

Explanation

Given Relation



`R={(1,1),(2,2),(3,3)}`



Reflexive: If a relation has `{(a, b)}` as its element, then it should also have` {(a, a),(b, b)} `as its elements too.


Symmetric: If a relation has `(a, b) `as its element, then it should also have `{(b, a)}` as its element too.


Transitive: If a relation has `{({a}, {b}),({b}, {c})}`as its elements, then it should also have `{({a}, {c})}` as its element too.


Now, the given relation satisfies all these three properties.

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