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.
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)
20. If p q is true and p is
true, then q is also true.
[(pq) ^ p] q
21. If p q and q r are true,
then p r is also true.
[(pq) ^ (qr)] (pr)
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
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.