Question

Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________
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Answer 1

SOLUTION

TO FILL IN THE BLANK

Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________

EVALUATION

Here the given set is S = {3, 5, 6}

Now the given relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)}

Now

1. R is reflexive

Since for every x ∈ S we have (x, x) ∈ R

2. R is symmetric

Since for x, y ∈ S and (x, y) ∈ R implies (y, x) ∈ R

3. R is transitive

Since for x, y, z ∈ S and (x, y) ∈ R and (y, z) ∈ R implies (x, z) ∈ R

Hence R is an equivalence relation

FINAL ANSWER

Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as Equivalence Relation

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Answer 2

Answer:

Step-by-step explanation:

it is reflexive only, not equivalence as (5,3) is present but not (3,5)