Mathematics - Algebra

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16. Match the following

A. Groups I. Associativity

B. Semi groups II. Identity

C. Monoids III. Commutative

D. Abelian Groups IV Left inverse

Codes. A B C D

Answer
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Option : A
Explanation :

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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, *) ?

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Option : D
Explanation :

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18. Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?

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Option : C
Explanation :

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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

Answer
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Option : A
Explanation :

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20. If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is

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Option : B
Explanation :

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