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propositions

A proposition is a declarative sentence that is either true or false. It cannot be a question, command, or exclamation. In logic and mathematics, propositions are the basic units whose truth values can be assigned. For example, "The earth orbits the sun" is a true proposition; "2+2=5" is a false proposition.

Not all sentences express propositions. Questions and imperatives do not have a truth value under standard

In propositional logic, propositions are combined with connectives to form compound propositions: and (conjunction), or (disjunction),

Beyond propositional logic lies predicate logic, which handles propositions with variables and quantifiers. In mathematics, a

two-valued
logic.
The
content
of
a
proposition
is
sometimes
called
its
meaning;
in
philosophy,
a
proposition
is
the
abstract
content
that
can
be
believed,
doubted,
or
asserted
independently
of
the
language
used
to
express
it.
not
(negation),
implies
(implication),
and
if
and
only
if
(biconditional).
These
connectives
are
truth-functional,
meaning
the
truth
value
of
the
compound
depends
on
the
truth
values
of
its
parts.
Truth
tables
express
all
possibilities;
tautologies
are
always
true,
contradictions
are
always
false,
and
logical
equivalence
means
two
propositions
share
the
same
truth
values
in
all
scenarios.
Satisfiability
means
there
exists
an
assignment
of
truth
values
making
a
proposition
true.
proposition
that
has
been
proved
is
called
a
theorem;
a
proposition
believed
to
be
true
but
not
yet
proven
is
a
conjecture.
Propositions
form
the
foundation
of
formal
reasoning
and
mathematical
proof.