Q. Determine
whether each of the following relations are reflexive, symmetric and
transitive:
(i)Relation
R in the set A
= {1, 2, 3…13, 14} defined as
R
= {(x,
y):
3x
− y
= 0}
(ii) Relation R in the set N
of natural numbers defined as
R
= {(x,
y):
y
= x
+ 5 and x
< 4}
(iii) Relation R in the set A
= {1, 2, 3, 4, 5, 6} as
R
= {(x,
y):
y
is divisible by x}
(iv) Relation R in the set Z
of all integers defined as
R
= {(x,
y):
x
− y
is as integer}
(v) Relation R in the set A
of human beings in a town at a particular time given by
(a) R
= {(x,
y):
x and
y
work at the same place}
(b) R
= {(x,
y):
x
and y
live in the same locality}
(c) R
= {(x,
y):
x is
exactly 7 cm taller than y}
(d) R
= {(x,
y):
x
is wife of y}
(e) R
= {(x,
y):
x
is father of y}
