Gate Exam

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

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Gate Other Question

Let X,Y,Z be sets of sizes x, y and z respectively. Let W = XxY and E be the set of all subsets of W. The number of functions from Z to E is:
(A) Z^2XY
(B) Zx^2
(C) Z^2XY
(D) 2XYZ 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