1. Using the axioms for a group determine which of the following are groups. State your reasoning (i) The set Q+ = {q = Q: q>0} under ×. (ii) The set Q+ = {q € Q : q > 0} under division. (iii) The set {1, 2, 3, 4, 5, 6, 7} under × mod 8. (iv) The set G = {( а -b b a b ) | ab € R ,bЄ R with a and b not both under matrix multiplication.
1. Using the axioms for a group determine which of the following are groups. State your reasoning (i) The set Q+ = {q = Q: q>0} under ×. (ii) The set Q+ = {q € Q : q > 0} under division. (iii) The set {1, 2, 3, 4, 5, 6, 7} under × mod 8. (iv) The set G = {( а -b b a b ) | ab € R ,bЄ R with a and b not both under matrix multiplication.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 4SE: Answer the following questions. 4. Describe how the permutation of ii objects differs from the...
Question
Transcribed Image Text:1. Using the axioms for a group determine which of the following are groups. State your reasoning
(i) The set Q+ = {q = Q: q>0} under ×.
(ii) The set Q+ = {q € Q : q > 0} under division.
(iii) The set {1, 2, 3, 4, 5, 6, 7} under × mod 8.
(iv) The set
G =
{(
а
-b
b
a
b ) | ab € R
,bЄ R with a and b not both
under matrix multiplication.
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