A proof aims to establish a fact by taking a proposition – conjecture – and applying by the mathematical axioms (given truths) establish a proved theorum. Induction is a general method for establishing a proof, and is usually used to establish that a proposition is true for any natural number.
A set is a collection of distinct objects considered as a whole.
[Wikipedia - http://en.wikipedia.org/wiki/Set ]
A set can be thought of as a collection of objects – or elements – and these objects can be anything, data – numerical – or indeed other sets. Elements in a set are in no particular order, and elements in a set must by definition be unique.
A Proposition is a declarative sentence, which may be shown to be either true, or false, whether the statement is true or false is not – however – relevant. Both “1+2-=3″ and “1+2=4″ are example of propositions. Predicate logic allows us to explore the truthfulness of a statement, it has an expressive power which propositional logic does not.