discrete mathematics

1. Complete: If a quantifier is applied to a predicate the resulting sentence will be ...... . 2. compound propositions are classified according to their possible truth values into a tautology, a contradiction or a contingency. Define these three terms and give only one example of each. Question # 2 1. By an argument, we mean a sequence of statements that end with a conclusion. Define what it means for an argument involving compound propositions to be valid. 2. Discuss briefly "The Rules of Inference for Propositional Logic" Question # 3 1. Mention the conditions on a function to be invertible and give examples to show the necessity of these conditions. 2. Define increasing and decreasing functions and give an example of an increasing function from R to itself that is not one-to-one. 3. Write the definition of a relation between two sets and state the difference between relations and functions