Reference no: EM131584698
1. In (Z x Z, o) ,the composition is defined by = (a, b) o (c, d) = (a -c, b - d) Where (a, b),(c, d) ∈ Z x Z. Is the composition is commutative and associative.
2. In (M2(R), *), the * is defined by A*B = (AB-BA)/2 .Is * is commutative and associative.
3. Let (G,*) is a group where * is defined by a*b = a o c o b for all a,b ∈ G.
Calculate the identity element of the group.
4. (P(X), *) is defined by A*B = A∩B for all A,B ∈ P(X).Check is it group or not?
Where P(X) is defined by the power set of X.
5. (P(X), *) is defined by A*B=A∪B for all A,B ∈ P(X).Check is it group or not?
Where P(X) is defined by the power set of X.
6. In a group G ,if a = a-1 for all a ∈ G, then show that G is a commutative group.
7. S is the set of 2 x 2 real matrices and binary operation * is defined on S by
A*B = (AB+BA) for all A,B ∈ S, then check that(S,*) is a semi group.
8. The set {1,2,3,5,7,8,9} under multiplication modulo 10 is not a group.Then justify
The options
a) It is not closed
b)2 does not have an inverse.
c) 3 has an inverse.
d) 8 does not have an inverse.
9. Prove that a group G is commutative if and only if (ab)-1 = a-1b-1 for all a,b ∈ G
10. Let G denote the set of all non zero real numbers. Define a binary operation * on G by
a*b = |a|b for all a,b ∈ G. Then is (G,*) a group?
|
How can we predict the next financial crisis
: The 2007-2008 financial crisis, you might think, was an unpredictable one-time crash. How can we predict the next financial crisis?
|
|
Explain how these are examples of that function
: Write up a description and explain how these are examples of that function.Determining what needs to be done, how it will b done, and whi is to do it.
|
|
What incentives influence firm to use international strategy
: What incentives influence firms to use international strategies? What are three basic benefit firms can achieve by successfully using an international strategy?
|
|
Gains to society and the marginal cost
: In the argument for why perfect competition is allocative efficient, the price that people are willing to pay represents the gains to society and the marginal.
|
|
Calculate the identity element of the group
: In (Z x Z, o) ,the composition is defined by = (a, b) o (c, d) = (a -c, b - d) Where (a, b),(c, d) ? Z x Z. Is the composition is commutative and associative.
|
|
Define two labeled infinite graphs
: Two labeled infinite graphs are shown in Figure. Show that they are isomorphic by defining a gipo between them and verifying that the gipo is an isomorphism.
|
|
Marginal propensity to import
: If NX = 95 when Y is 0, and m (marginal propensity to import) is 0.025, solve for X
|
|
Examine the fundamental aspects of innovation
: Examine the fundamental aspects of innovation that either support or do not support the overall retailer-consumer relationship.
|
|
Goodwill write-offs indicate about leadership decisions
: What do goodwill write-offs indicate about leadership decisions?
|