Find all of the elements in the subgroup K = ((12)(34), (125)) < $5.
(a) List all the generators of < 5 > in Z6o. (b) List all of the left cosets of < 10 > in the subgroup < 2 > of Z60.
12) Let U ={NEN:n <200} , find the number of elements of U that are divisible by 2, 3, or 7.
5. Suppose H and K are subgroups of G and H 10, and |K-21. Prove that 6. Consider the subgroup <3 > of Z12. Find all the cosets of < 3>. How many distinct cosets are there?
+ for (a)0</zl</ (6) 12/> 1. -6) Find the two Laurent series in powers of z that represent sin --
(a) List all the generators of < 5 > in Z60. (b) List all of the left cosets of < 10 > in the subgroup < 2 > of Z60. 7. (7 points each) (a) List all the generators of <5> in Z6o. (b) List all of the left cosets of <10 > in the subgroup < 2 > of Z60-
Find all real solutions of the equation (2 – 6)? = 4. 21 = and 12 with i < 22
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
For a standard normal distribution, find: P(Z < c) = 0.2523 Find c.
For a standard normal distribution, find: P(0.61 < z < 2.92)
Find the general solution. 11. r'(t) = (1 -3)<< (t)