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.