Let G be a group of order 40 whose subgroups include H and K, of orders 4 and 5, respectively. (a) State whether each of the following statements is true or false, justifying your answers. (i) G has an element of order 1. (ii) G has an element of order 2. (iii) G has an element of order 3. (iv) G has an element of order 5. (b) Prove that HnK = {e}, where e is the identity element of G.

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