Answer:
Let
A = {5, 6, 7}
(i) Let R =
{(6, 7), (7, 6)}
Clearly, R is
symmetric.
As (5, 5) and (6, 7) and
(7, 6)
but (6, 6)
R is neither
reflexive nor transitive.
(ii) Let R = {(5, 6),
(5, 7), (7, 6)}
Clearly, R is
transitive.
As (5, 5)
R and (5, 7)
but (7, 5)
R
R is neither
reflexive nor symmetric.
(iii) Let R = {(5,
5), (6, 6), (7, 7), (5, 6), (6, 5), (6, 7),
(7, 6)}
Clearly, R is
reflexive and symmetric.
As (5, 6) and (6,
7)
but (5, 7)
is not
transitive.
(iv)Let R = {(5,
5), (6, 6), (7, 7), (5, 6)}
Clearly, R is
reflexive and transitive.
As (5,6)
but (6, 5)
is not
symmetric.
(v) Let R = {(5,
6), (6, 5), (5, 5), (6, 6)}
Clearly, R is
symmetric and transitive.
As (7, 7)
R is not
reflexive.
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