Come up with 1 set with an operation that is a group. i.e., itmust have the four
ID: 3093575 • Letter: C
Question
Come up with 1 set with an operation that is a group. i.e., itmust have the four properties of: 1) the set is a closed under the operation 2) the set is associative under the operation 3) the set has the identity element under the operation thatis also an element of the set 4) every element of the set has an inverse under the operationthat is also an element of the setI need an actual set, i.e, {1,3,5,7} btw, my textbook 'Mathematiecal Ideas' is not listed!! -- Ilisted 'Algrbra 2' from the drop down because it won't let me postif I don't select something. Same is true for 'Course'. thanks! Come up with 1 set with an operation that is a group. i.e., itmust have the four properties of: 1) the set is a closed under the operation 2) the set is associative under the operation 3) the set has the identity element under the operation thatis also an element of the set 4) every element of the set has an inverse under the operationthat is also an element of the set
I need an actual set, i.e, {1,3,5,7} btw, my textbook 'Mathematiecal Ideas' is not listed!! -- Ilisted 'Algrbra 2' from the drop down because it won't let me postif I don't select something. Same is true for 'Course'. thanks!
Explanation / Answer
On the set {1,3,5,7} define the binary operation as ab mod8.This givesus * 1 3 5 7 1 1 3 5 7 3 3 1 7 5 5 5 7 1 3 7 7 5 3 1 this is the operationtable. We can see that the operation is closed on the set, it isassociative as regular multiplication mod an integer isassociative. We can see that the identity is 1. The inverse of 1 is 1, the inverse of 3 is 3, the inverse of 5is 5 and the inverse of 7 is 7.