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11 . Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then
A. < A, * > is a monoid but not a group
B. < A, * > is a group but not an abelian group
C. < A, * > is a semi group but not a monoid
D. A is closed under * but < A, * > is not a semi group

12 . Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?
A. (Z, *) is a group
B. (Z, *) is a monoid
C. (Z, *) is an abelian group
D. None of these

13 . Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?
A. G is of finite order
B. g = g² for every g ∈ G
C. g = g-1 for every g ∈ G
D. (g o h)² = g²o h² for every g,h ∈ G

14 . If the binary operation * is deined on a set of ordered pairs of real numbers as (a,b)*(c,d)=(ad+bc,bd) and is associative, then (1, 2)*(3, 5)*(3, 4) equals
A. (7,11) B. (23,11)
C. (32,40) D. (74,40)

15 . If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is
A. reflexive B. transitive
C. symmetric D. not anti-symmetric




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