Propositional Logic and Mathematical Induction Help please :)

Basically I have recently started a new course and Have had these questions set as examples, The notes do not explain thoroughly enough and I can't get my head round what to do, I can't even understand what is said on Google, could someone show me how to do these questions in step by step easy English, It would be greatly appreciated.

1st Example:

http://i279.photobucket.com/albums/kk138/GazMor/1.jpg

2nd Example:

http://i279.photobucket.com/albums/kk138/GazMor/2.jpg

Thank you in advance

Ga.