Discrete Math (Logical Connectives)

AND

True only if both propositions are true.

OR

True if at least one of the propositions is true.

NOT

True if the proposition is false.

Implications

False only if the first proposition is true and the second is false.

Biconditional

True if both propositions have the same truth value.

Tautology

A tautology is a logical statement that is true in every possible situation or under every possible interpretation of its variables.

Contradiction

A contradiction is a logical statement that is false in every possible situation or under every possible interpretation of its variables.

communitive law

the order of the operands does not affect the outcome. For both addition and multiplication, this law holds

Identity Law

the identity element for the operation leaves the other element unchanged, with "true" as the identity for logical AND and "false" as the identity for logical OR

Complement Law

the logical AND or OR of a variable with its complement resulting in the constants true or false, respectively

Conditional Identity

identities involving conditional expressions can relate to logical implications or the properties of conditional probabilities.

Distributive Law

relate to how multiplication and addition interact over sets or in algebra.

De Morgan's law

the complement of the union of two sets is equal to the intersection of their complements, and vice versa

Predicate

A predicate is a function or expression involving variables that becomes a proposition when those variables are substituted with specific values, thus assigning it a truth value.

Proposition

A proposition is a declarative statement that is either true or false, but not both. It has a definite truth value.

Universal Quantifier (∀)

This symbol, which looks like an upside-down "A," stands for "for all" or "for every." It is used to express that a predicate or statement is true for every element of a certain set.

Existential Quantifier (∃)

This symbol, which might look like a backward "E," means "there exists." It is used to state that there is at least one element in a specified set for which the predicate or statement is true.