Test by Bikram | Mock GATE | Test 2 | Question: 39

Question

A relation can be defined by giving the ordered pairs of elements for which the relation holds.

Let $R$ be defined over $\left \{ a,b,c \right \}$ by $R$ $=$ $\left \{ \left ( a,a \right )\left ( a,b \right ) \left ( b,a \right )\left ( b,b \right )\left ( c,c \right )\right \}$.

Which of the following properties does $R$ have?

1. Symmetry
2. Antisymmetry
3. Reflexivity
4. Transitivity

• A. II and III only
• B. II and IV only
• C. I, III, and IV
• D. II, III, and IV

Answer 1

Here we can check pretty simply,that all property given is satisfied except Antisymmetry

According to the definition of Antisymmetric relation

for every X,Y belongs toa a relation R , is Antisymmetric if the following condition satisfied

if(xRy) and (yRx) then X=Y

here (a,a)(b,b,)(c,c) satisfying it  but there is (a,b)(b,a) but a not equal to b..so not satisfying

....so  C is correct answer here