Discrete Mathematics

what is a logical connective

its used to create a compound proposition from two or more other propositions

what is Negation?

the opposite of the original statement

what is Conjunction-Logical AND?

The conjunction p ^ q is true when both p and q are true and is false otherwise

what is disjunction (logical "or")

the disjunction p v q is false when both p and q are false and is true otherwise

what is Exclusive OR?

the exclusive or of these two proposition is true when exactly one of p and q is true ; it is false when both p and q are true , and when both are false (p XOR q)

what's a conditional statement

the conditional statement "if p, then q" is false when p is true , and q is false , and true otherwise because it asserts that q is true on the condition that p holds

what's conserve, and contrapositive. and inverse?

conserve is "if q, then p"

contrapositive is "if not q, then not p" has the same truth value as "If p, then q " and is false only when not q is false and not p is true

inverse is "If not p, then not q"

the conserve and the inverse are both true when p is true and q is false and is false otherwise

Explain what is Biconditional

the proposition "p if and only if q" is true when p and q have the same truth values and is false otherwise

Bitwise Operations?

a bit can be used to represent a truth value 1 represents T (true) , 0 represents F (false)

Logical connectives can be applied to bit strings (of equal length). To do this, we simply apply the connective rules to each bit of the string

what are the three logical connectives in a Bitwise Operation?

bitwise OR, bitwise AND, and bitwise XOR

Define Compound propostion

•to refer to an expression formed from propositional variables using logical operators, such as p ∧ q.

Define tautology

A compound proposition that is always true, no matter what the truth values of the propositional variables that occur in it

Define contradiction

A compound proposition that is always false

Define contingency

A compound proposition that is neither a tautology nor a contradiction

Define Logical Equivalences

•if p ↔ q is a tautology. The notation p ≡ q denotes that p and q are logically equivalent

what is Predicate logic?

its where you cannot adequately express the meaning of all statements in mathematics and in natural language.

What is a Quantifier?

to create a proposition from a proposition function

what are the 2 types of quantifiers?

Universal Quantification and Existential Quantification

What does Universal Quantification do?

tells us that a predicate is true for every element under consideration

What does Existential Quantification?

tells us that there is one or more element under consideration for which the predicate is true.

What is Nested Quantifiers?

Where one quantifier is within the scope of another

What is Rule of Interference?

To establish the validity of some relatively simple argument forms