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Transcript
Statements
Some sentences can be evaluated as true or false. Example:
"He" is the president of the USA.
If we replace "He" by Barack Obama, then the sentence has a truth-value of true. But if we replace "He" by James Rodriguez then the truth-value of the sentence is false.
It is a statement when we can know the truth-value of the statement.
Negation Of a Statement
You just have to insert the word " not" en the resulting statement is the opposite. Example:
- Original Statement: Sunday is the day after Saturday
- Negation: Sunday is not the day after Saturday
Conjunction
Two statements connected by the word and.
p: 9>7
q:7=(2x3) + 1
Conjunction p/\ q
9>7 and 7= (2x3) + 1
It is true because both statements are true.
p/\q is true when p and q are both true and false when at least one of the statements p or q is false
Disjunction
Two statements are connected by the word: or
p: a ray has two endpoints
q: 120 ÷ 6= 20
Disjunction p \/ q
a ray has two endpoints or 120 ÷ 6 = 20
It is true because since one of the statements is true
p\/q is true when at least one of the statements p or q is true and it is false when p and q are both false
Conditional
If p then q
Statements:
p: I study
q: Mr Perez will pass me
Conditional p->q ( p implies q)
If I study, then Mr Perez will pass me
p->q is false when the hypothesis is true and the conclusion is false.
Bi-conditional
p if and only if q
The bi-conditional statement is true when both statements p and q are true or when statements p and q are false
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Let's review
http://www.quia.com/rr/243312.html
http://www.softschools.com/quizzes/language_arts/statement_or_question/quiz1525.html
http://www.ixl.com/math/geometry/truth-tables
Compound statements