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Previous Year Question (PYQs)

Consider the following properties:

A. Reflexive
B. Antisymmetric
C. Symmetric

Let $A=\{a,b,c,d,e,f,g\}$ and

$R=\{(a,a),(b,b),(c,d),(c,g),(d,g),(e,e),(f,f),(g,g)\}$

be a relation on $A$. Which of the following property/properties is/are satisfied by the relation $R$?




Solution

For reflexive relation, every element must have pair $(x,x)$.

But $(c,c)$ and $(d,d)$ are missing.

So, relation is not reflexive.

For antisymmetric relation, if $(x,y)$ and $(y,x)$ both exist, then $x=y$.

Here, no reverse pair exists for $(c,d),(c,g),(d,g)$.

So, relation is antisymmetric.

For symmetric relation, if $(x,y)$ exists, then $(y,x)$ must also exist.

But $(c,d)$ exists and $(d,c)$ does not exist.

So, relation is not symmetric.

Therefore, relation satisfies B and not A.

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