LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
in Mathematics by (34.1k points)

Let R be a relation in the set of integer I defined by aRb iff a & b both are neither even nor odd. Then show that R is symmetric but neither reflexive nor transitive.

1 Answer

+1 vote
by (37.1k points)
selected by
Best answer

Given relation aRb is defined only when, both a & b are not even or odd at a time.

i.e., if a is even & b is odd then aRb is well defined.

(i) Let a and be odd and even then aRb is defined and aRb ⇒ bRa

Hence, R is symmetric.

(ii) Let a be an odd then aRa is not defined and a be an even then also aRa is not defined.

So, R is not reflexive.

(iii) Let a and b be odd and even respectively. Then if R is transitive, then aRb, bRa ⇒ aRa but, then aRa is not defined as a is odd. Hence, R is not transitive.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.