DISCRETE MATHEMATICS

Discrete Mathematics

is a branch of mathematics that deals with the study of finite objects that is an object that can be counted

Logic

is an art or science of correct or valid reasoning.

proposition

is any simple (also called atomic) declarative statement that is either true or false, yes or no, 1 or 0 but not both

tautology

A compound proposition (or compound statement) that is true for all possible truth values of its constituent propositional variables is called a

contradiction

A compound proposition that is false for all possible truth values of its constituent propositional variables is called a

contingency

A compound proposition that is neither a tautology nor a contradiction – whose truth tables exhibit some T and some F entries – is called a

CONVERSE OF P → Q

Q → P

INVERSE OF P → Q

~ P →~ Q

CONTRAPOSITIVE OF P → Q

~ Q →~ P

predicate

Let P(x) be the statement involving x , and U, called the universe of discourse, be the set for which x can be taken from. P(x) is called a

Instantiation and Quarification

2 ways of transforming a propositional function into a proposition

Universal quantifier

denoted by ∀, is used for propositional functions involving the keywords every, each, any, all, for every, for each, for any, or for all.

existential quantifier

denoted by ∃, is used for propositional functions involving the keywords some, there is, at least one, for some, for few, or for at least one.

Euler Diagrams

Validity of most quantified arguments may also be verified using graphical representations involving circles (or ellipses), which are very similar to Venn diagrams. ______, named after Leonhard Euler, are used for this purpose.