Evaluate whether the following propositions are true or false.Prove if true, counter-example if false, or prove falseshow me.(a) A 200-membered group has a 25-element normal subgroup. (b) There are...

Evaluate whether the following propositions are true or false. Prove if true, counter-example if false, or prove false show me. (a) A 200-membered group has a 25-element normal subgroup. (b) There are a total of 2 different homomorphisms from Z10 to Z2 (c) There is no one-to-one homomorphism from S5 × Z3 × Z3 to S12.