Solution to Let A = {1,2,3,4}. Define a relation R on A by a R b ↔ … - Sikademy
Author Image

Archangel Macsika

Let A = {1,2,3,4}. Define a relation R on A by a R b ↔ a + b ≤ 4 for every a; b ϵ A. (a) List all the elements of R. (b) Determine whether R has the following properties. If R has a certain property, prove this is so, otherwise, provide a counterexample to show that it does not. i. Reflexivity ii. Transitivity iii. Antisymmetry iv. Symmetry

The Answer to the Question
is below this banner.

Can't find a solution anywhere?


Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Given, A=\{1,2,3,4\} and R=\{(a,b):a+b \leq 4\}.

a) The elements of the relation R is, R=\{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)\}.


i) R is not reflexive, since (3,3)\notin R

ii) R is not transitive, since (2,1)\in R, (1,3)\in R, but (2,3) \notin R

iii) R is not anti-symmetry, since (1,2)\in R, (2,1)\in R, but 1\neq 2.

iv) For each (a,b)\in R , we have (b,a)\in R. Hence, R is symmetry.

Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-3872-qpid-2571