Statements & Truth Tables• True or False• This statement is true or false.?• A T/F statement is a declarative sentence.• It has a value of true or false, but not both at the same

time.• Thus the following two statements are equivalent:

This statement is false.This statement is true and this statement is false.

The latter is a simple contradiction of the form "A and not A", and hence is false.

TF Statements• The sentence “Today is Thursday” is a TF

statement since we can decide whether the sentence is true or false.

• The sentence “Lincoln was the first President of the United States” is a TF statement since we can decide whether the sentence is true or false.

• “Is it a bear?” is not a TF statement since it is a question, not a simple declarative sentence.

• “Sit down” is not a TF statement. It is a command, not a simple declarative sentence.

TF Statements/Negations• To negate a TF statement is to change its truth value.• Negated by using the word not or ~ Let p: I get paid on Friday.Then, ~p: It is not true that I get paid on Friday,or simply “I don’t get paid on Friday”. Let e:Europe is a city.Therefore ~e: It is not true that Europe is a city,or simply “Europe is not a city”.

p ~pT FF T

TF Statements/Conjunctions• Join two TF statements by the word and.• The symbol for the conjunction is ^. Let b: Jordan plays basketball. Let c: Jordan stars in TV commercials.The conjunction “Jordan plays basketball and stars in TV commercials” is written symbolically as b^c.

TF Statements/Disjunctions• Join two TF statements by the word or.• The symbol for the conjunction is ˅. Let p: I will pass this CST121. Let s: I will go to summer school.The disjunction “I will pass this CST121 or I will go to summer school” is written symbolically as p ˅ s.