DISCRETE MATHEMATICS PLEASE HELP ME?!! Let A = {1, 2, 3}. (a) Give an example of
ID: 3141054 • Letter: D
Question
DISCRETE MATHEMATICS PLEASE HELP ME?!!
Let A = {1, 2, 3}. (a) Give an example of a relation R_1 on the set A such that R_1 is reflexive, but is neither symmetric nor transitive. Briefly explain why your relation is neither symmetric nor transitive. (b) Give an example of a relation R_2 on the set A such that R_2 is symmetric, but is neither reflexive nor transitive. Briefly explain why your relation is neither reflexive nor transitive. (c) Give an example of a relation R_3 on the set A such that R_3 is transitive, but is neither reflexive nor symmetric. Briefly explain why your relation is neither reflexive nor symmetric. If you think that one of these combinations is impossible, justify your answer by clearly explaining why no relation on the set A could meet the required combination of conditions.Explanation / Answer
(a) R = {(1,1),(2,2),(3,3),(1,3),(3,2)}
The relation is reflexive as (1,1),(2,2) and (3,3) all exist.
The relation is not symmetric as (1,3) exists but (3,1) does not.
The relation is not transitive as (1,3) and (3,2) exist but (1,2) does not.
(b) R = {(1,1),(3,3),(2,1),(1,2)}
The relation is not reflexive as (2,2) does not exist.
The relation is symmetric as (2,1) and (1,2) both exist.
The relation is not transitive as (2,1) and (1,2) exist but (2,2) does not.
(c) R = {(1,1),(2,2),(1,2),(2,3),(1,3)}
The relation is not reflexive as (3,3) does not exist.
The relation is not symmetric as (1,2) exists but (2,1) does not.
The relation is transitive as (1,2),(2,3) and (1,3) exist. As do (1,2),(2,2) and (2,2).
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