subpropositional parts. These subpropositional parts have meanings of their own, like referring to objects
or classes of objects.[51] Whether the simple proposition they form is true depends on their relation to
reality, i.e. what the objects they refer to are like. This topic is studied by theories of reference.[52]
Some complex propositions are true independently of the substantive meanings of their parts.[53] In
classical logic, for example, the complex proposition "either Mars is red or Mars is not red" is true
independent of whether its parts, like the simple proposition "Mars is red", are true or false. In such cases,
the truth is called a logical truth: a proposition is logically true if its truth depends only on the logical
vocabulary used in it.[54] This means that it is true under all interpretations of its non-logical terms. In
some modal logics, this means that the proposition is true in all possible worlds.[55] Some theorists define
logic as the study of logical truths.[16]
Truth tables can be used to show how logical connectives work or how the truth values of complex
propositions depends on their parts. They have a column for each input variable. Each row corresponds to
one possible combination of the truth values these variables can take; for truth tables presented in the
English literature, the symbols "T" and "F" or "1" and "0" are commonly used as abbreviations for the
truth values "true" and "false".[56] The first columns present all the possible truth-value combinations for
the input variables. Entries in the other columns present the truth values of the corresponding expressions
as determined by the input values. For example, the expression " " uses the logical connective 
(and). It could be used to express a sentence like "yesterday was Sunday and the weather was good". It is
only true if both of its input variables,  ("yesterday was Sunday") and  ("the weather was good"), are
true. In all other cases, the expression as a whole is false. Other important logical connectives are  (not),
 (or),  (if...then), and  (Sheffer stroke).[57] Given the conditional proposition , one can form
truth tables of its converse , its inverse ( ), and its contrapositive ( ). Truth tables
can also be defined for more complex expressions that use several propositional connectives.[58]
Truth table of various expressions
p q p ∧  q p ∨  q p → q ¬p → ¬q p  q
T T T T T T F
T F F T F T T
F T F T T F T
F F F F T T T
Logic is commonly defined in terms of arguments or inferences as the study of their correctness.[59] An
argument is a set of premises together with a conclusion.[60] An inference is the process of reasoning
from these premises to the conclusion.[43] But these terms are often used interchangeably in logic.
Arguments are correct or incorrect depending on whether their premises support their conclusion.
Premises and conclusions, on the other hand, are true or false depending on whether they are in accord
with reality. In formal logic, a sound argument is an argument that is both correct and has only true
premises.[61] Sometimes a distinction is made between simple and complex arguments. A complex
Logical truth
Truth tables
Arguments and inferences