Question

Let A = { a,b,c } and a relation R is defined on set A as R = { (a,a), (b,c) , (a,b) } . Write the minimum number of ordered pairs to be included in relation R to make it both reflexive and symmetric.

Answer 1

ANSWER

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.The the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b)}.

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.The the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b)}.Now this relation is reflexive but not transitive as (a,b)∈A,(b,c)∈A⇒(a,c)

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.The the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b)}.Now this relation is reflexive but not transitive as (a,b)∈A,(b,c)∈A⇒(a,c)

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.The the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b)}.Now this relation is reflexive but not transitive as (a,b)∈A,(b,c)∈A⇒(a,c)∈A.

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.The the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b)}.Now this relation is reflexive but not transitive as (a,b)∈A,(b,c)∈A⇒(a,c)∈A.Now to make this relation to be transitive we are to add (a,c).

ANSWERGiven the relation the relation R be defined on A as follows R={(a,a),(b,c),(a,b)}.Now, to make this relation R to be reflexive we are to add the elements like (x,x) for all x∈A.The the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b)}.Now this relation is reflexive but not transitive as (a,b)∈A,(b,c)∈A⇒(a,c)∈A.Now to make this relation to be transitive we are to add (a,c).Then the relation will be R={(a,a),(b,b),(c,c),(b,c),(a,b),(a,c)}