Chapter 1 SETS, FUNCTIONs, ELEMENTARY LOGIC & BOOLEAN ALGEBRAs. BY: MISS FARAH ADIBAH ADNAN IMK. 1.3 ELEMENTARY LOGIC. 1.3.1 INTRODUCTION. 1.3.2 PROPOSITION. CHAPTER OUTLINE: PART III. 1.3.3 COMPOUND STATEMENTS. 1.3.4 LOGICAL CONNECTIVES. 1.3.5 CONDITIONAL STATEMENT.
Chapter 1SETS, FUNCTIONs, ELEMENTARY LOGIC & BOOLEAN ALGEBRAs
BY: MISS FARAH ADIBAH ADNAN
1.3 ELEMENTARY LOGIC
CHAPTER OUTLINE: PART III
1.3.3 COMPOUND STATEMENTS
1.3.4 LOGICAL CONNECTIVES
1.3.5 CONDITIONAL STATEMENT
1.3.6 PROPOSITIONAL EQUIVALENCES
John is smart or he studies every night.
The truth value is determined by the truth value of its subpropositions, together with the way they are connected to form compound proposition.
1) Not (negation) : ~ /
Let p be a proposition. The negation of p is denoted by
, and read as “not p”.
Find the negation of the preposition “Today is Friday”.
The Truth Table for the Negation of a Preposition
2) And (conjunction) :
Let p and q be prepositions. The preposition of “p and q” - denoted , is TRUE when BOTH p and q are true and otherwise is FALSE.
The Truth Table for the Conjunction of Two Prepositions
3) Or (disjunction) :
Let p and q be prepositions. The preposition of “p or q” - denoted , is FALSE when BOTH p and q are FALSE and TRUE otherwise.
The Truth Table for the Disjunction of Two Prepositions
Consider the following statements, and determine whether it is true or false.
Let p and q be the following propositions:
p = It is below freezing
q = It is snowing
Translate the following into logical notation, using p and q and logical connectives.
1) Conditional Statement/ Implication
Let p and q be a preposition. The implication is the preposition that is FALSE when p is true, q is false. Otherwise is TRUE.
p = hypothesis/antecedent/premise
q = conclusion/consequence
Express: “ if p, then q”, “q when p”, “p implies q”
The Truth Table for the Implication ( )
2) Equivalence/ Biconditional
Let p and q be a preposition. The biconditional is the preposition that is TRUE when p and q have the same truth values, and FALSE otherwise.
Express: “ p if and only if q”
The Truth Table for the Biconditional ( )
CONVERSE : the implication of is called converse of
CONTRAPOSITIVE : the contrapositive of is the implication
Example: refer textbook
Example: refer text book
Two propositions p and q are said to be logically equivalent, or simply equivalent or equal, denoted by
if they have identical truth tables.
Example: Find the truth tables of