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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
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B
symmetric
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C
transitive
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D
equivalence
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Solution

The correct options are
A symmetric
B reflexive
Distance 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 symmetric

Mathematics

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