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CONDITIONAL
STATEMENTS
CONDITIONAL STATEMENT
A conditional statement is a
statement in IF and THEN form. The
IF part is called the hypothesis and...
CONDITIONAL STATEMENT
IF A, then B.
A  B
If you buy a lipstick in the right place,
then it’s OK to buy the wrong lipstick.
Hypothesis: You buy a lipstick in the
right place.
Conclusion: It is OK to buy the wrong
lipstick.
NEGATION
The negation of A is “not A”.
~A means “not A”.
S: It is raining today.
~S: It is not raining today.
TRUTH VALUE
Truth value of a statement is
either TRUE or FALSE.
(Valid vs. Invalid)
TRUTH VALUE
A: 2011 is the year of the
rabbit.
Truth value: TRUE
B: Water is solid.
Truth value: False
TRUTH VALUE
A statement and its negation
have different truth value.
B: A frog is a bird. (FALSE)
~B: A frog is not a bird...
DERIVED STATEMENTS
CONDITIONAL INVERSE
A  B ~A  ~B
CONVERSE CONTRAPOSITIVE
B  A ~B  ~A
THEOREM
A conditional and its
corresponding contrapositive are
logically equivalent. (Same truth
value). The converse and ...
BICONDITIONAL
CONDITIONAL
A  B (TRUE)
CONVERSE
B  A (TRUE)
BICONDITIONAL
A <--> B
BICONDITIONAL
BICONDITIONAL
A <--> B
A if and only if B.
DEDUCTIVE
REASONING
If p  q is true and p is
true, then q is also true.
[(pq) ^ p]  q
If p  q and q  r are true,
then p  r is also true.
[(pq) ^ (qr)]  (pr)
All AA students are female.
“If a student is an AA student, then the student is a
female.” (TRUE)
FACT/Given: Sam is an AA...
All AA students are female.
“If a student is an AA student, then the student is a
female.” (TRUE)
All females have XY chro...
PROVING
To prove a conjecture, we apply
deductive reasoning.
To prove something we need to supply a proof.
Truth is based on solid...
A group of algebraic steps used to solve
problems form a deductive argument.
A two-column proof, or formal proof, contains
statements and reasons organized in two columns.
04 geom cond
04 geom cond
04 geom cond
04 geom cond
04 geom cond
04 geom cond
04 geom cond
04 geom cond
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Transcript of "04 geom cond"

  1. 1. CONDITIONAL STATEMENTS
  2. 2. CONDITIONAL STATEMENT A conditional statement is a statement in IF and THEN form. The IF part is called the hypothesis and the THEN part is called the conclusion.
  3. 3. CONDITIONAL STATEMENT IF A, then B. A  B
  4. 4. If you buy a lipstick in the right place, then it’s OK to buy the wrong lipstick.
  5. 5. Hypothesis: You buy a lipstick in the right place. Conclusion: It is OK to buy the wrong lipstick.
  6. 6. NEGATION The negation of A is “not A”. ~A means “not A”. S: It is raining today. ~S: It is not raining today.
  7. 7. TRUTH VALUE Truth value of a statement is either TRUE or FALSE. (Valid vs. Invalid)
  8. 8. TRUTH VALUE A: 2011 is the year of the rabbit. Truth value: TRUE B: Water is solid. Truth value: False
  9. 9. TRUTH VALUE A statement and its negation have different truth value. B: A frog is a bird. (FALSE) ~B: A frog is not a bird. (TRUE)
  10. 10. DERIVED STATEMENTS CONDITIONAL INVERSE A  B ~A  ~B CONVERSE CONTRAPOSITIVE B  A ~B  ~A
  11. 11. THEOREM A conditional and its corresponding contrapositive are logically equivalent. (Same truth value). The converse and inverse of a conditional are logically equivalent. (Same truth value)
  12. 12. BICONDITIONAL CONDITIONAL A  B (TRUE) CONVERSE B  A (TRUE) BICONDITIONAL A <--> B
  13. 13. BICONDITIONAL BICONDITIONAL A <--> B A if and only if B.
  14. 14. DEDUCTIVE REASONING
  15. 15. If p  q is true and p is true, then q is also true. [(pq) ^ p]  q
  16. 16. If p  q and q  r are true, then p  r is also true. [(pq) ^ (qr)]  (pr)
  17. 17. All AA students are female. “If a student is an AA student, then the student is a female.” (TRUE) FACT/Given: Sam is an AA student. (TRUE) Conclusion: Sam is female. (TRUE) by Law of Detachment
  18. 18. All AA students are female. “If a student is an AA student, then the student is a female.” (TRUE) All females have XY chromosomes. “If you are female, then you have XY chromosomes.” Conclusion: If a student is an AA student, then the student has XY chromosomes.. (TRUE) by Law of Syllogism AA  F and F  XY therefore AA  XY
  19. 19. PROVING
  20. 20. To prove a conjecture, we apply deductive reasoning. To prove something we need to supply a proof. Truth is based on solid evidences (proofs). A proof is a logical argument in which each statement you make is supported by a statement that is accepted as true Forms of Proof in Geometry INFORMAL – essay form of a proof; spontaneous and descriptive/narrative FORMAL – organized and well-structured
  21. 21. A group of algebraic steps used to solve problems form a deductive argument.
  22. 22. A two-column proof, or formal proof, contains statements and reasons organized in two columns.
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