symbolic logic
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SYMBOLIC LOGICStatemen
tConnectiv
esQuantor validity
How to prove?
SYMBOLIC LOGIC
Statement
Open Sentenc
e
Variable &
Constanta
Statement
Connectives
Quantor validityHow to prove?
SYMBOLIC LOGIC
Statement
Open Sentenc
e
Variable &
Constanta
A statement is a declarative sentence, which is to saya sentence that is capable of being true or false.The following are examples of statements.
it is rainingI am hungry2+2 = 4God exists
On the other hand the following are examples of sentences that are not statements.
are you hungry?shut the door, please#$%@!!! (replace ‘#$%@!!!’ by your favorite expletive)
Statement
Connectives
Quantor validityHow to prove?
SYMBOLIC LOGIC
Variable is a symbols which is point to
unspecified members of the universal
Constant is a symbol which is point to
specific element in the universal
Example:
An straight line equation y = 2x + 3
Which one are variables or constant?
Statement
Connectives
Quantor validityHow to prove?
Statement
Open Sentenc
e
Variable &
Constanta
SYMBOLIC LOGIC
Open sentence is a sentence with variables and
if the variables was substituted with the constat
in the universal then you can determine it is true
statement or wrong statement
Statement
Connectives
Quantor validityHow to prove?
Statement
Open Sentenc
e
Variable &
Constanta
SYMBOLIC LOGICStatemen
tConnectiv
esQuantor validity
How to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
SYMBOLIC LOGIC
Negation
Conjunction
Disjungtion
Implication
Biimplication
A (statement) connective is an expression
with one or more blanks (places) such that,
whenever the blanks are filled by statements the
resulting expression is also
a statement.
Simple statement is a a statement that is not
constructed out of smaller statements by the
application of a statement connective
Compound statement is a statement that is
constructed from one or more
simplestatements by the application of a
statement connective.
Statement
Connectives
Quantor validityHow to prove?
SYMBOLIC LOGIC
Negation of a statement is a new statement
which is true if the truth of the first statement is
false and conversely.
Symbolized by : or ¬ or ~
Means: “ not”, “no”, “it is not true (false) that”,
“it cannot be that”, it is imposible that”, etc
Example:
1. p :This two things are similar
2. ~p: this two things are not simmilar
Statement
Connectives
Quantor validityHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
SYMBOLIC LOGIC
This issummarized in the following truth tables.
Note: ~d has the opposite truth value of d.
p ~ p
B S
S B
Statement
Connectives
Quantor validityHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
SYMBOLIC LOGIC
Disjunction is corresponds roughly to the English ‘or’.The symbol for disjunction is “ ˅ “ (wedge).In English, the word ‘or’ has at least two different meanings, or senses, which are respectively called the exclusive sense and the inclusive senseSo there are two types of disjunction:1. Inclusive DisjunctionA disjunction p ˅ q is false if both disjuncts are false;otherwise, it is true
2. Exclusive DisjunctionA disjunction p ˅ q is false if both disjuncts are the same truth; otherwise, it is true
Statement
Connectives
Quantor validityHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
SYMBOLIC LOGIC
Conjunction is corresponds to the English
expression ‘and’.
The symbol for conjunction is “ ˄ “
Deffinition:
A conjunction p ˄ q is true if both conjuncts are
true;
otherwise, it is false
Statement
Connectives
Quantor validityHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
SYMBOLIC LOGIC
the conditional connective is corresponds to the
expression
if ___________, then ___________.
The symbol used to abbreviate if-then is the
arrow (→)
‘if’ introduces the antecedent
‘then’ introduces the consequent
A conditional d → f is false if the antecedent d is
true and the consequent f is false; otherwise, it is
true.
Statement
Connectives
Quantor validityHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
SYMBOLIC LOGIC
the biconditional is corresponds to the
English
______________if and only if _______________
The symbol for the biconditional connective is ‘
↔ ’
A biconditional d ↔ e is true if its constituents
have the same truth value; otherwise,it is false
Statement
Connectives
Quantor validityHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
Statement
Connectives
QuantorHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
Statement
Connectives
QuantorHow to prove?
Negation
Conjunction
Disjungtion
Implication
Biimplication
