Question

# The relation $$R=\left \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\right \}$$ on the set $$A=\left \{1,2,3\right \}$$ is

A
reflexive but not symmetric
B
reflexive but not transitive
C
symmetric and transitive
D
neither symmetric nor transitive

Solution

## The correct option is A reflexive but not symmetricWe have $$A=\left \{1,2,3\right \}$$ and $$R=\left \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\right \}$$.Since $$(1,1), (2,2), (3,3)\in R$$, $$R$$ is reflexiveR is not symmetric because $$(1,2)\in R$$ and $$(2,1)\not {\in}R$$.R is transitive because $$(1,2), (2,3)\in R$$ and $$(1,3)\in R$$.$$\therefore$$ The correct answer is $$A$$.Mathematics

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