Gate Exam

A relation R is defined on ordered pairs of integers as follows:
(x,y)R(u,v)if x < u andy> v. Then R is:
(A) Neither a Partial Order nor an Equivalence Relation
(B) A Partial Order but not a Total Order
(C) A Total Order
(D) An Equivalence Relation

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Gate Other Question

The set {1,2,3,5,7,8,91 under multiplication modulo 10 is not a group. Given
below are four plausible reasons. Which one of them is false?
(A) It is not closed
(B) 2 does not have an inverse
(C) 3 does not have an inverse
(D) 8 does not have an inverse For each element in a set of size 2n,an unbiased coin is tossed. The 2ncoin tosses are
independent. An element is chosen if the corresponding coin toss were head. The probability
that exactly n elements are chosen is: