UGC NET CSE | December 2019 | Part 2 | Question: 5

Question

Let $P$ be the set of all people. Let $R$ be a binary relation on $P$ such that $(a, b)$ is in $R$ if $a$ is a brother of $b$. Is $R$ symmetric transitive, an equivalence relation, a partial order relation?

• A. $\text{NO, NO, NO, NO}$
• B. $\text{NO, NO, YES, NO}$
• C. $\text{NO, YES, NO, NO}$
• D. $\text{NO, YES, YES, NO}$

Answer 1

The correct answer is Option (A).

 

Symmetric: aRb => bRa

x is a brother of y. So x should be brother of x which is not necessary. y might be a sister of x.

Therefore, R is not symmetric relation.

 

Transitive:  aRb and bRc imply aRc

x is a brother of y, y is a brother of x, but x is not a brother of x.

Therefore, R is not a transitive relation.

 

Equivalence: The relation must be reflexive, transitive, and symmetric.

But, R is not satisfied with any of the 3 relation properties.

Therefore, R is not an equivalence relation.

 

Partial Order: The relation must be reflexive, transitive, and anti-symmetric.

But, the R is neither reflexive nor transitive.

Therefore, R is not a partial order relation.

 

So, the correct answer is NO, NO, NO, NO.

 

 

Comments

This answer is wrong. The correct answer is No,YES,NO,NO

since it is a transitive relation, xRy means x is the brother of y and yRz means y is brother of z, so surly x is the brother of z.