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How do you feel about part a?

I do not fully know how to complete part b

Okay, to find the converse do I assume a disjoint cycle and show that it is an involution?

yes, exactly

that's only one way

Okay. SO that is saying that we have an involution sigma^2=(1) and leading to disjoint 2 cycles?

maybe it would help if you did it the other way too. S
o I can see the entire picture

That makes more sense now. Thanks a ton!