Q1: Choose the Correct Answer from the Following Sentences: 1. In the group (Z20, +20), the...

 

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Q1: Choose the Correct Answer from the Following Sentences: 1. In the group (Z20, +20), the order of the element 10 is A. 4 C. 6 2.In the commutative group (G,*), the value of (ab-¹)-¹ ==-------- A. ba B. b-¹a C. a-¹b D. ba-1 B.8 D. 2 3.The elements generate the group (Z9, +9) are:------ A. {1,2,4,5,} B. {1,2,4,5,7,8} 2. [G: H]. C. {3,4,5,6) (6 Marks) Q2: Fill in the Blanks in the Following Sentences 1. The elements generate the group (Z11, +11) are:------- 2. (Z,.)is not a group since 3.Suppose that (G,*) is a group such that G = {(a, b): a, b € R, a # 0}, and * defined as, (a, b) (c,d) = (ac, bc + d), then (a, b)-¹=------ Q3: (3 Marks) Let G = (Z24, +24), and H 1.The left cosets of H in G. {0,8, 16) is a sub group of G, find D. {2,3,4,5,6) (6 Marks) Q1: Choose the Correct Answer from the Following Sentences: 1. In the group (Z20, +20), the order of the element 10 is A. 4 C. 6 2.In the commutative group (G,*), the value of (ab-¹)-¹ ==-------- A. ba B. b-¹a C. a-¹b D. ba-1 B.8 D. 2 3.The elements generate the group (Z9, +9) are:------ A. {1,2,4,5,} B. {1,2,4,5,7,8} 2. [G: H]. C. {3,4,5,6) (6 Marks) Q2: Fill in the Blanks in the Following Sentences 1. The elements generate the group (Z11, +11) are:------- 2. (Z,.)is not a group since 3.Suppose that (G,*) is a group such that G = {(a, b): a, b € R, a # 0}, and * defined as, (a, b) (c,d) = (ac, bc + d), then (a, b)-¹=------ Q3: (3 Marks) Let G = (Z24, +24), and H 1.The left cosets of H in G. {0,8, 16) is a sub group of G, find D. {2,3,4,5,6) (6 Marks)

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