EXERCISE 1
1. Consider the following properties of relations : Symmetric (S), Transitive (1), Reflexive
(R), Equivalence (E), None of these (N).
State which property/properties are satisfied by each of the following relations:
(Give the answers in terms of S, T, R, E and N).
(a) "is greater than" for the set of real numbers.
(6) "is the cube of" for the set of all real numbers.
(C) “is the sister of" for a set of children.
(d) "is similar to" for the set of triangles.
(e) "is perpendicular to” for a set of co-planar lines.
Answers
Answered by
4
(A) S
(B) N
(C) R
(D) N .!
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yashsarankarpaj57u:
c and d
how can they be equivalance relation
R= sister of. a is sister of herself. so it is reflexive. a is sister of b then bis sister of a so R is symmetric. a is sister of b, b is sister of c, then a is sister of c, then R is transitive. Hence R is reflexive, symmetric and transitive. There fore R is equivalence relation.
similarly do d
if b is boy then b is not sister of a so it is not symmetric relation .
you are correct. The set consists of children. they may be boys and girls.
In that case it is not equivalence relation. it is possible only all are girls.
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