Geometry unit 2
If a statement is true, then its negation is
false
Negation
if p is a statement, the new statement, not p or p is false is called the negation of p
What conclusion can be based on the given statement? q is a whole number between 42.3 and 43.1
q = 43.0
The converse of p —> q is
q —> p
Conjunction:
statement formed by combining two statements with the word and "^"
Hypothesis:
the "if" portion of your conditional statement; what your conditional statement is about
Conclusion
the "then" portion of your conditional statement; what your conditional statement is doing
Hypothesis
the if clause in a statement
Truth value:
the status of a statement as either true or false
Conclusion
the then clause in the statement Conditional or implication: two statements connected by the form "if...then..."
Contrapositive:
this version of the conditional combines the converse with the inverse and switches the hypothesis and conclusion while negating both portions
Inverse:
this version of the conditional negates both the hypothesis and the conclusion portions of the statement
Converse:
this version of the conditional switches the hypothesis portion with conclusion portion of the statement
disjunction of P and q
p v q
or
v
not
~
P: 6 + 3 = 12
~ P: 6 + 3 =not 12
The inverse of p —> q is
~p —> ~q
The contrapositive of p —> q is
~q —> ~p
The inverse of x —> y is
~x —> ~y
Conjecture:
a conclusion that is formed based on observation
A proposition is a statement that will be true or false but not both EXAMPLE
"That person is an infant." A simple strategy to verify the statement is to look at the person. At this time, you are not concerned with whether or not the proposition is true or false, only that it can be verified to be either true or false.
Select whether the following statement is always true, sometimes true, or never true. (The hypothesis of a statement is the if part.)
Always
statement is always true, sometimes true, or never true. (In a proof the figure should fit the hypothesis.)
Always
statement is always true, sometimes true, or never true. (The conclusion of a statement is the then part.)
Always
Select inductive reasoning, deductive reasoning, or neither. If 5x + 7 = 12, then x = 1.
Deductive reasoning
What is the truth value for the following conditional statement? p = false q = false p —> q
F F —> T
What is the truth value for the following conditional statement? p = true q = true ~q —> ~p
F F —> T
What is the truth value for the following conditional statement? p = false q = true ~q —> ~p
F T —> T
What is the truth value for the following conditional statement? p = true q = true ~p = q
F T —> T
Which statements has the same truth value as the statement "If it is Friday, then Bruce has beans for supper.?
If Bruce does not have beans for supper, then it is not Friday.
What is the contrapositive of the given statement? (If dogs have fleas, they scratch all night.)
If they don't scratch all night, then dogs don't have fleas.
Sentence 1: its raining Sentence 2: the ground is wet
Its raining and the ground is wet
What is the truth value for the following conditional statement? p = true q = false p —> q
T F —> F
If p is a true statement and q is false, what is the truth value of p v q?
T F —> T
What is the truth value for the following conditional statement? p = false q = flase ~ p = ~q
T T —-> T
What is the truth value for the following conditional statement? p = true q = true p —> q
T T —> T
Given the following two statements, what conclusion can be made? 1. Three noncollinear points determine a plane. 2. Points S, O, N are noncollinear.
The points S, O.N form a plane
Contrapositive
When p —> q is a conditional, a new conditional can be formed by interchanging the hypothesis and the conclusion and negating both of them g - p is the new conditional formed. It is called the contrapositive of the conditional.
And
^
Conditional statement:
a logical statement that is broken down into two parts, the hypothesis and the conclusion
Statement:
a sentence based of mathematical theory; used to prove logical reasoning
True-False statement:
a sentence based on mathematical theory that is true or false, but not both
Disjunction:
a statement formed by combining two statements with the word or
Counterexample:
an example that proves a conjecture is a false statement
You _____ always prove a conclusion by inductive reasoning.
cannot
When two statements are connected with the word and, the new statement is called a
conjunction
Where p and q are statements, p ^ q is called the of p and q
conjunction
When two statements are connected with the word or, the new statement is called a
disjunction
Where m and n are statements m y is called the of m and n.
disjunction
contradiction
is a proposition, or statement that is always false. EXAMPLE: 5 ≠ 5.
tautology
is always true. EXAMPLE: the statement 5 = 5.
