ASPIRE EN MATH Search 179 pages Q ATIOSTROUS Homework 3: Due Friday January 15th by 9:00 a.m.ecit Problemi 1. Describe all of the symmetries of this shape Then make cool symbols like we did for the equilateral triangle and then compule all combinations of two symmetries using cool rules like you made for the equilateral triangle [Be sure to list the rules! Problem 2: Assume that you have the following Rules Rule 1 Associativity Rule 2 18 = $1 = Sfor any symmetry S Rule 3: FF Rule 4. RRR = 1 Now prove that the rules RF - FRR and (FR)(FR) - 1 are equivalent. DO THE PROOF(S) IN TWO WAYS Use the method where you start with one side of the rule to be proved and manipulate it to get the other side (using the assumed rule at some point) Use the method where you start with the assured rule and manipulate it to get the rule to be proved. Note: Yes, this means you will do proofs since proving two rules are equivalent means proving each one implies the other Jyou are doing we proofs and doing each of the two ways). They are good for you and less filling Homework 6: Due Wednesday January 20th by 9:00 a.m. O edit Homework 7: Due Monday January 25th by 9:00 a.m.ccit ASPIRE EN MATH Search 179 pages Q ATIOSTROUS Homework 3: Due Friday January 15th by 9:00 a.m.ecit Problemi 1. Describe all of the symmetries of this shape Then make cool symbols like we did for the equilateral triangle and then compule all combinations of two symmetries using cool rules like you made for the equilateral triangle [Be sure to list the rules! Problem 2: Assume that you have the following Rules Rule 1 Associativity Rule 2 18 = $1 = Sfor any symmetry S Rule 3: FF Rule 4. RRR = 1 Now prove that the rules RF - FRR and (FR)(FR) - 1 are equivalent. DO THE PROOF(S) IN TWO WAYS Use the method where you start with one side of the rule to be proved and manipulate it to get the other side (using the assumed rule at some point) Use the method where you start with the assured rule and manipulate it to get the rule to be proved. Note: Yes, this means you will do proofs since proving two rules are equivalent means proving each one implies the other Jyou are doing we proofs and doing each of the two ways). They are good for you and less filling Homework 6: Due Wednesday January 20th by 9:00 a.m. O edit Homework 7: Due Monday January 25th by 9:00 a.m.ccit