Answer:
Step-by-step explanation:
We are given that G be a finite group with have two elements of order two.
We have to prove that <x,y> is either abelian or isomorphic to a dihedral group.
<x,y> means the group generated by two elements of order 2.
We know that is a cyclic group and number of elements of order 2 is always odd in number and generated by one element .So , given group is not isomorphic to
But we are given that two elements of order 2 in given group
Therefore, group G can be or dihedral group
Because the groups generated by two elements of order 2 are and dihedral group.
We know that is abelian group of order 4 and every element of is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be also generated by two elements of order 2
Hence, <x,y> is isomorphic to or .
Step-by-step explanation:
a(n) = a +(n-1)d
d=1/4 -1/2 =-1/4
°.° a(15) = 1/2 +(15–1) -1/4
a(15) = 1/2 -3.5
=<u>-3</u>
<u>hope it will help</u>
FOIL stands for first, outer, inner, and last.
So, you multiply the first terms together, the outer terms together, the inner terms together, and then the last terms together.
(b+3)(b-9)
b^2-9b+3b-27 Then simplify
b^2-6b-27
East because it is the dimesndion of the quadrilateral