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UGC NET Paper1 June 2015 /  UGC NET Computer Science June 2015

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# Set Theory and Algebra MCQ >

## Set Theory and Algebra MCQ

Partial Ordering , Lattice and Boolean Algebra
Sets

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

 A. IV   I    II   III B. III    I   IV   II C. II   III   I   IV D. I    II    III   IV

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, *) ?

 A. (Z, *) is a monoid B. (Z, *) is an abelian group C. (Z, *) is a group D. None of these

18:

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

 A. g = g-1 for every g ∈ G B. g = g2 for every g ∈ G C. (g o h) 2 = g2o h2 for every g,h ∈ G D. 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

 A. (74,40) B. (32,40) C. (23,11) D. (7,11)

20:

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

 A. not anti-symmetric B. transitive C. reflexive D. symmetric