16. For the given relation R on a set S, determine which
are equivalence relations :
(a) (1) S is the set of all rational numbers, aRb iff
a= b
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(ii) S is the set of all real numbers aRb iff
(I) la l =1b1
(II) a 2 b.
(b) (i) S is the set of all triangles in a plane, arb
iff a is congruent to b
(ii) S is the set of all triangles in a plane, aRb
iff a and b have equal perimeters
(iii) S is the set of all people in India today, aRb
iff a and b have same mother-tongue
(iv) S is the set of all people in the world
today, aRb iff a and b have same mother-
tongue
(v) S is the set of all people in the world
today, aRb iff a lives within 75 kilometres
from b.
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cet A
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