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41 Cards in this Set

  • Front
  • Back
"Conditional" statement
"if-then" statement
if xxxxx, then yyyy
if "hypothesis", then "conclusion.
Q: Truth value of conditional statement
True -- everytime the hypothesis is true, then the conclusion is also true.
False - show that ONLY ONE counter-example showing hypothesis true and conclusion is false
Q: Hypothesis and Conclusion within a conditional statement.
Hypothesis is the "if" part;
Conclusion is the "then" part.
Converse of a Conditional statement
Reverse the if, then parts.
conditional: if xxx, then yyy.
converse: if yyy, then xxx.
Biconditional statement.
The statement you get by connecting the conditional and it's converse with "and".

The "converse" IF AND ONLY IF the "conditional"
Deductive (logical) reasoning
The process of reasoning logically from given statements to reach a conclusion.
Law of Detachment
If a conditional is true and it's hypothesis is true, then it's conclusion is true.
Law of Syllogism
If p, then q AND if q, then r are true
if p, then r is also true.
(2-3)Symbolic way of writing a conditional statement
p --> q.
means; if p , then q.
Q: Description of Law of Syllogism
allows you to state a conclusion from --
- two true conditional statements, when the conclusion of one statement is the hypothesis of the other
Q: What types of statements make up the law of syllogism
two conditional statements:

conditional (p --> q)
conditional (q --> r)
Q: write the law of syllogsm (2-3) given:
if a number is prime, then it does not have repeated factors.
if a number does not have repeated factors, then it is not a perfect square.
p - number is prime
q - does not have repeated factors
r -- is not a perfect square.
if a number is prime, then it is not a perfect square
Addition property
if a=b, then a+c = b+c
Subtraction property
if a=b, then a-c = a-b
multiplication property
if a=b, then a*b = b*c
division property
if a=b and c NE 0, then a/c - b/c
reflexive property
(2-4) Symmetric property
if a=b, then b=a
(2-4) Transitive property
if a=b and b=c, then a=c
(2-4) substitution property
if a=b, then b can replace a in any expression
(2-4) distributive property
a (b+c) = ab + ac

41 = 40+1
3(41) = 3(40) + 3(1).
(2-4 distributive property
ab + ac = a(b+c)
a is distributed across b & c.
(2-1) angle addition postulate
the sum of the small angles making a large angle = the large angle.
(2-1) angle bisector
A line bisecting (i.e. cutting in half) an angle results in two equal angles whos sum equals the original angle.
(2-1) segment addition postulate
the sum of the small segments making a large segment = the large segment.
(2-4) reflexive property
line ab CG to line ab
angle a CG to angel a
(2-4) symmetric property
if line ab CG to cd, then cd is CG to ab.
if angle a CG to angle B, then angle B CG angle A
q: paragraph proof
a proof written as sentences in a paragraph.
q: theorem
the statement that you prove, via a set of steps
a series of steps , using deductive reasoning.
q: postulate
a proposition that is accepted as true in order to provide a basis for logical reasoning
(A self-evident or universally recognized truth)
q: what are the steps in making a proof.
1) list everything that is given.
2) list what you must show (prove).
3) list the steps (assumptions, postulates) to get to the proof).
q: What is the vertical angles theorem?
Vertical angles are congruent.
q: prove that vertical angles are congruent.
L1 and L2 are vertical angels
L1 = L2
L1 +L3 = 180 angle addition p
L2 +L3 = 180 angle addition p
L1 +L3 = L2+L3 -subs
L1 = L2 sub L3 both sides
q: if 2 angles are supplements of the same angle (or of congruent angles), then the 2 angles are congruent.
L1 and L2 are suppl.
L3 and L2 are suppl
L1 = L3
L1 + L2 = 180 defn suppl
L2 + L3 = 180 defn supp
L1 + L2 = L2+L3 subst
L1 + L3 subtr L2
2-5 how is a theorem different than a postulate
A postulate is assumed true.
A theorem is proven true by steps based on deductive reasoning.
is this a good definition? why not.
A pencil is a writing instrument
if a pencil is an instrument than it is for writing.
if it is used for writing it is an instrument.
q: what makes a "good" definition - 3 items
1) uses clearly understood or defined terms.
2) precise (not large, sort of, almost..).
3) reversible -- can write it as a biconditional.
4) no counter-examples.
q: what is meant by reversible
can be written as a true biconditional.

the conditional and the converse are true. p if and only if q.
q: write the statements that form the biconditonal for:
two angles are congruent if and only if they have the same measure
if two angles are congruent, then they have the same measure.

if two angles have the same measure than they are congruent.
q: is this a good definition - why / why not.
A cat is an animal with whiskers.
A counterexample is a dog which has whiskers.
if an animal is a cat than it has whiskers.
if an animal has whiskers it is a cat.