Use induction to prove the sum principle for n finite

Question

Question: 1. Use induction to prove the sum principle for n finite sets.

2. Show that if z ∈ Z and z² | z, then z ∈ {-1,0,1}.

3. If three cats like tuna, five cats like salmon, two cats like both tuna and salmon, and one cat does not like fish at all, how many cats have been consulted?

4. Find χ(G) and χ' (G) for the two graphs shown in Figure.