Question

3 Let A = {p, q, r). Which of the following is
an equivalence relation on A?
Choose an option:
Ry = {(p, q), (q, r), (p, r) (p, p)}
R2 = {(1,9), (rp), (r, 1) (q, 9)}
R3 = {(p.p), (q,9), (r,() (p, q)}​

Answer 1

Answer:

Solution

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Correct option is

D

None of these

Given A={p,q,r}

R

1

={(p,q),(q,r),(p,r),(p,p)}

R

1

is not reflexive as it does not have (q,q),(r,r) . So, R

1

is not an equivalence relation on A.

R

2

={(r,q),(r,p),(r,r),(q,q)}

R

2

is not reflexive as it does not have (p,p) . So, R

2

is not an equivalence relation on A.

R

3

={(p,p),(q,q),(r,r),(p,q)}

R

3

is reflexive but not symmetric as (p,q) is there ,but not (q,p)