1. CONDITIONAL
STATEMENTS

3. 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.

4. CONDITIONAL STATEMENT
IF A, then B.
A  B

5. If you buy a lipstick in the right place,
then it’s OK to buy the wrong lipstick.

6. Hypothesis: You buy a lipstick in the
right place.
Conclusion: It is OK to buy the wrong
lipstick.

7. NEGATION
The negation of A is “not A”.
~A means “not A”.
S: It is raining today.
~S: It is not raining today.

8. TRUTH VALUE
Truth value of a statement is
either TRUE or FALSE.
(Valid vs. Invalid)

9. TRUTH VALUE
A: 2011 is the year of the
rabbit.
Truth value: TRUE
B: Water is solid.
Truth value: False

10. 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)

12. DERIVED STATEMENTS
CONDITIONAL INVERSE
A  B ~A  ~B
CONVERSE CONTRAPOSITIVE
B  A ~B  ~A

15. 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)

17. BICONDITIONAL
CONDITIONAL
A  B (TRUE)
CONVERSE
B  A (TRUE)
BICONDITIONAL
A <--> B

18. BICONDITIONAL
BICONDITIONAL
A <--> B
A if and only if B.

19. DEDUCTIVE
REASONING

20. If p  q is true and p is
true, then q is also true.
[(pq) ^ p]  q

21. If p  q and q  r are true,
then p  r is also true.
[(pq) ^ (qr)]  (pr)

22. 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

23. 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

24. PROVING

25. 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

26. A group of algebraic steps used to solve
problems form a deductive argument.

27. A two-column proof, or formal proof, contains
statements and reasons organized in two columns.