1.

Determinewhether each of the following relations are reflexive, symmetric andtransitive:(i)RelationR in the set A= {1, 2, 3…13, 14} defined as R= {(x,y):3x− y= 0}(ii) Relation R in the set Nof natural numbers defined asR= {(x,y):y= x+ 5 and x< 4}(iii) Relation R in the set A= {1, 2, 3, 4, 5, 6} asR= {(x,y):yis divisible by x}(iv) Relation R in the set Zof all integers defined asR= {(x,y):x− yis as integer}(v) Relation R in the set Aof human beings in a town at a particular time given by(a) R= {(x,y):x andywork at the same place}(b) R= {(x,y):xand ylive in the same locality}(c) R= {(x,y):x isexactly 7 cm taller than y}(d) R= {(x,y):xis wife of y}(e) R= {(x,y):xis father of y}

Answer»

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}


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