Questions
1
A non empty set A is termed as an algebraic structure ________
Answer: with respect to binary operation *
7
The set of all real numbers under the usual multiplication operation is not a group since
Answer: zero has no inverse
8
The inverse of - i in the multiplicative group, {1, - 1, i , - i} is
Answer: i
9
If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an
Answer: abelian group
10
If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is
Answer: transitive
11
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: (74,40)
12
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: IV I II III
17
If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an
Answer: abelian group
18
If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is
Answer: abelian group
19
The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is
Answer: -1
