The science of clear thinking and correct reasoning, logic is used to determine the relations between statements, and to
obtain conclusions from true statements.
A statement is any sentence that is either TRUE or FALSE, but not both.
Truth value – the truth or falsity of a statement.
To save time and space, statements are often represented using a letter such as p, q, or r.
P: Upper Dublin High School is located in Fort Washington.
The negation of a statement has the opposite meaning as well as the opposite truth.
Compound Statement – joining two or more statements
The logical AND
Symbols:
For a conjunction to be true, BOTH p AND q must be true.
p: Cardinals are the UDHS mascot.
q: Our colors are cardinal and grey at UDHS.
p
q:
the logical AND is commutative!
Determine the Truth Value of Conjunctions:
p: A linear pair of angles is supplementary.
q: October has 31 days.
r and q:
r: Bill Clinton is our President.
~r and p:
p and q:
~q and r:
The logical OR
A disjunctions is a compound statement formed by joining two or two or more statements with the word “or”
Symbol:
A disjunction is true if at LEAST one of the statements is true.
p:
q:
EX) Use the following statements to write a compound statement for each disjunction. Then find its truth value.
̅̅̅̅ is proper notation for “line AB”
p: 𝐴𝐵
q: Centimeters are metric units
r: 9 is a prime number
a) p or q
b) p and r
c) p or r
d) q or r
VENN DIAGRAMS
Illustrate both conjunctions and disjunctions.
Truth Table – a convenient method for organizing the values of statements
The number of rows is determined by 2𝑛 , where n is the number of variables (statements)\
Generic Truth Tables:
2 statements:
3 statements:
After the base is constructed, you add columns as you need them until your statement is complete!
Draw a truth table to show all possible outcomes of 𝑝 ⋀ (~𝑞 ⋁ 𝑟)