Consider the following relation Ron a set A R={(a,a) (a,b) (b,a) (b,b) (b,c) (cc) } Consider the following statements Stat 1: R is an equivalence relation Stat 2: R is not an equivalence relation because it is not transitive Stat 3: R is not an equivalence relation because it is not symmetric Stat 4: Adding just one ordered pair to R can make the new relation equivalence relation Choose the correct statements a) Stat 1 is True and Stat 4 is true b) Stat 2 is true c)Stat 4 is false d) Stat 3 is false d)Stat 3 is false a) Stat 1 is True and Stat 4 is true b)Stat 2 is true

Question

ZariaZ2098 ZariaZ2098

07-09-2019
Mathematics

contestada

Consider the following relation Ron a set A R={(a,a) (a,b) (b,a) (b,b) (b,c) (cc) } Consider the following statements Stat 1: R is an equivalence relation Stat 2: R is not an equivalence relation because it is not transitive Stat 3: R is not an equivalence relation because it is not symmetric Stat 4: Adding just one ordered pair to R can make the new relation equivalence relation Choose the correct statements a) Stat 1 is True and Stat 4 is true b) Stat 2 is true c)Stat 4 is false d) Stat 3 is false d)Stat 3 is false a) Stat 1 is True and Stat 4 is true b)Stat 2 is true

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Answer with Step-by-step explanation:

We are given that a relation on set A

R={(a,a),(a,b),(b,a),(b,b),(b,c),(c,c)}

We have to tell which statement is true about the given relation.

We know that if relations is reflexive, symmetric and transitive then the relation is called equivalence relation.

Reflexive:if (a,a) is present in the given relation for every element a belongs to A.

Symmetric :If (a,b) are present in the relation the (b,a) is also present in the given relation for every ordered pair (a,b) belongs to R.

Transitive: If (a,b) and (b,c) are present in the given relation then (c,a) is also present in the given relation.

Therefore, given relation is reflexive .

Given relation is not symmetric and not transitive because (c,b) and (c,a) are not present in the given relation.Therefore, relation is not equivalence.

Therefore,

Option

(a) Stat 2 : true .

(c) Stat 4: False Because we need two ordered pair to make the equivalence relation.