Statements
Definition of a Statement
A declarative sentence that is either true or false, but not both true and false. Questions and commands are not statements.
Simple Statements
Simple statements do not have a connective. Connectives are also called operators.
Categorical
The copula is a state of being verb.
p is q
all p is q
p is not q
no p is q
some p is q
some p is not q
For more detail take the Statement Parts and Types links at the left.
Compound Statements
Two or more simples statements, typically designated by the letters p, q, r and s, that are connected by (have a copula of) one or more logical operators (connectives).
Negation ( ~ ) [A fundamental operator]
For the negation connective used with a single term see Negation. Negation of compound statements is on that page and is directly linked to from the page on each compound statement.
Conjunctive (p ^ q) [A fundamental operator]
p and q
Disjunctive (p v q) [A fundamental operator]
p or q
All of the following are derived from the three fundamental operators above.
Strong Disjunctive (p |v| q)
Either p or q but not both
Negative Disjunctive
Neither p nor q
Hypothetical (Conditional) (p -> q}
If p then q
q, if p
p, only if q
All p are q
Strong Hypothetical (Biconditional) (p <-> q)
p if and only if q
q if and only p
If p then q, and conversely
If q then p, and conversely
Hypothetical Negative
No p is q
If p then not q
Casual
p because q
Prohibitive
p unless q
unless q, p
