Question

# Let $$S$$ be the set of all points in a plane and $$R$$ be a relation in $$S$$ defined as  $$R = \{(a, b) :$$  distance between points $$a$$ and $$b$$ is less than $$2$$ units $$\}$$The relation $$R$$ is

A
reflexive
B
symmetric
C
transitive
D
equivalence

Solution

## The correct options are A symmetric B reflexiveDistance between $$a$$ and $$a$$ is $$0,$$ which is less than $$2$$ units.$$R$$ is reflexive.If $$(a,b) \in R$$, then distance between $$a$$ and $$b$$ is less than $$2$$ units$$\Rightarrow$$ Distance between $$b$$ and $$a$$ is less than $$2$$ units$$(b,a) \in R$$$$\therefore R$$ is symmetricMathematics

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