Ch. 7 Flashcards
conjunction
“and”, ^, true when both statements r true
disjunction
“or”, V, true when @ least 1 statement is true
negation
~, “not”
Inclusive “Or”
doing 1/other/both
4 ways to rewrite p –> q
If p, then q Every p has q The fact that p implies that q p iff q
converse
q –> p
inverse
~p –> ~q
contrapositive
~q –> ~p
Direct Argument
p –> q
p
… q
Indirect Argument
p –> q
~q
… ~p
Chain Rule
p –> q
q –> r
… p –> r
Or Rule
p V q
~p
…q
p V q
~q
… p
Venn diagram placement for conditionals/implications
biconditional rules
p iff q
q
… p
p iff q
p
… q
p iff q
~p
… ~q
p iff q
~q
… ~p
good definition
built from a true conditional with a true converse
two-column proof
a proof written in 2 columns. statements are listed in 1 column & justifications r listed in the other column
paragraph proof
a proof whose statements & justifications r written in paragraph form
flow proof
a proof written as a diagram using arrows to show the connections b/w statements. #’s written over the arrows refer to a #-ed list of the justifications 4 the statements
postulate
a statement assumed to be true w/out proof
Addition Property of Equality
If the same # is added to equal #’s, the sums r equal a = b –> a + c = b + c
Subtraction Property of Equality
If the same # is subtracted from equal #’s, the differences r equal. a = b –> a - c = b - c
Multiplication Property of Equality
If equal #’s r multiplied by the same #, the products r equal a = b –> ac = bc
Division Property of Equality
If equal #’s are divided by the same nonzero #, the quotients are equal. a = b and c_0 –> a/c = b/c
Reflexive Property of Equality
A # is equal to itself. a = a
Substitution Property
If values are equal, 1 value may be substituted 4 the other. a = b –> a may be substituted 4 b
Distributive Property
An expression of the form a(b + c) is equivalent to ab + ac. a(b + c) = ab + ac
square root
one of 2 equal factors of a #
straight angle postulate
If the sides of an angle form a straight line, then the angle is a straight angle with a measure of 180
Angle or Segment Addition Postulate (Whole and Parts Postulate)
For any segment or angle, the measure of the whole is equal to the sum of the measures of its non-overlapping parts.
Supplements of Angles Theorem (7.1)
If 2 angles are supplementary to the same angle, then they are equal in measure.
Complements of Angles Theorem (7.2)
If two angles are complements of the same angle, then they are equal in measure.
Vertical Angle Theorem
All vertical angles are equal in measure.
Corresponding Angles Postulate (Post. 10)
If 2 parallel lines r intersected by a transversal, then corresponding angles are equal in measure.
Alternate Interior Angles Th (Th 7.4)
If 2 parallel lines r intersected by a transversal, then alternate interior angles are equal in measure.
what kinds of angles are these?
angles 3 and 6 are alternate interior angles
angles 1 and 8 are alternate exterior angles
angles 3 and 5 are cointerior angles
angles 2 and 6 are corresponding angles
Co-Interior Angles Th (Th 7.5)
If 2 parallel lines are intersected by a transversal, then co-interior angles are supplementary.
What kinds of angles are shown below?
Angles A and D are consecutive angles.
Angles A and C are opposite angles.
Consecutive Angles Th (Th 7.6)
If a quadrilateral is a parallelogram, then consecutive angles are supplementary.
Opposite Angle Theorem (Th 7.7)
If a quadrilateral is a paralleogram, then opposite angles are equal in measure.
Venn diagram placement for biconditionals
hypothesis
The if part of an if-then statement
conclusion
The then part of an if-then statement.
implication/conditional
A statement with an if part and a then part.
premise
A given statement in an argument. The resulting statement is called the conclusion.
valid argument
An argument that uses rules of logic.
biconditional
the conjunction of a true conditional and its true converse, usually written using the phrase if and only if
