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16. Match the followingA. Groups I. AssociativityB. Semi groups II. IdentityC. Monoids III. Commutative D. Abelian Groups IV Left inverseCodes. A B C D
IV I II III
III I IV II
II III I IV
I II III IV
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17. 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, *) ?
(Z, *) is a monoid
(Z, *) is an abelian group
(Z, *) is a group
None of these
18. Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?
g = g-1 for every g ∈ G
g = g2 for every g ∈ G
(g o h) 2 = g2o h2 for every g,h ∈ G
G is of finite order
19. 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
(74,40)
(32,40)
(23,11)
(7,11)
20. If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is
not anti-symmetric
transitive
reflexive
symmetric
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