Which of the following statements is/are true?
a) There are infinitely many finite groups in which every non-identity element have order $2$.
b)There exists an infinite group in which every non-identity element have order $2$.
c)There exists an infinite group in which there are elements of order $n$ for all $n\in \Bbb N$.
d)There are infinitely many infinite groups in which each non-identity element have finite order.
My attempt: Option 2 seems correct as I have an example of such a group( Power set of Natural numbers under the binary operation of symmetric difference is one such example) but I am unable to conclude anything about other options.
About option 1, it seems that it is true keeping in mind $\Bbb Z_2\times \Bbb Z_2\times\cdots$ but still I am confused. For the last two options, I don't have any conclusive idea which I can apply here. Please guide.