Discrete Quiz

DSTL QUIZ 3

UNIT 2 : ALGEBRAIC STRUCTURES

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CS( New Branch)

Q1: The set of all real numbers under the usual multiplication operation is not a group since *

1 point

A. multiplication is not a binary operation

B. multiplication is not associative

C. identity element does not exist

D. zero has no inverse

Q2.If * is defined on R* as a * b = ab/ 2,' then identity element in the group (R*., *) is *

1 point

A .1

B. 2

C. 1/2

D.1/3

Q3. The inverse of - i in the multiplicative group, {1, - 1, i , - i} is *

1 point

A. 1

B. -1

C. i

D. -i

Q4. The set of all nth roots of unity under multiplication of complex numbers form a/an *

1 point

A. semi group with identity

B. commutative semigroups with identity

C. group

D. abelian group

Q5. Every cyclic group is _____. *

1 point

(A) a group with finite order

(B) a group with prime order

(C) a non Abelian group

(D) an Abelian group

Q6. Suppose (2, 5, 8, 4) and (3, 6) are the two permutation groups that form cycles. What type of permutation is this? *

1 point

a) odd

b) even

c) acyclic

d) prime

7. Which of the following is not subgroup of (R,+) *

1 point

A) (ℤ, +)

(B) (ℚ, +)

(C) (ℝ, +)

(D) (C,+)

Q8. If H1 and H2 are subgroups of the group G, then which one of the following is also a subgroup of G? *

1 point

(A) H1∪H2

(B) H1∩H2

(C) H1∆H2

(D) None of these

Q.9. For G= (ℤ5, +5),WHERE Z5={0,1,2,3,4} and (with addition modulo 5) how many generators of the cyclic group G? *

1 point

Q10. A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called _____________ *

1 point

a) isomorphic

b) homomorphic

c) cyclic group

d) heteromorphic

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