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26. If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is
symmetric only
anti-symmetric only
both symmetric and anti-symmetric
an equivalence relation
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27. Which of the following statements is true?
Every equivalence relation is a partial-ordering relation.
Number of relations form A = {x, y, z} to B= (1, 2), is 64.
Empty relation φis reflexive
Properties of a relation being symmetric and being un-symmetric are negative of each other.
28. Let A = {1, 2, .....3 }Define ~ by x ~ y ⇔ x divides y. Then ~ is
reflexive, but not a partial-ordering
symmetric
a partial-ordering relation
29. G (e, a, b, c} is an abelian group with 'e' as identity element. The order of the other elements are
2,2,3
3,3,3
2,2,4
2,3,4
30. If every element of a group G is its own inverse, then G is
finite
infinite
cyclic
abelian 133.
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