EMATH REVIEWER Flashcards
MEANS TO DEMONSTRATE THE TRUTH OR EXISTENCE OF
(SOMETHING) BY EVIDENCE OR ARGUMENT.
PROVING
IS A DEVICE USED TO ESTABLISH THE ABSOLUTE AND IRREVOCABLE
TRUTH OF STATEMENTS IN MATHEMATICS
PROOF
The science of correct reasoning.
Logic
The drawing of inferences or conclusions
from known or assumed facts.
Reasoning
a combination of two statements p (hypothesis) and q (conclusion) and by the words “if” and “then”. It comes in the form “if p, then q.”
Conditional statement
A conditional statement is also called an?
Implication
How to write an if-then statement?
- find the subject and predicate
- then place the subject in the if part of the sentence
- then put a comma
- then put the predicate in the then part of the sentence then period.
a figure , an explanation or a situation used to justify that a given conditional is false.
COUNTEREXAMPLE
IS THE TRANSFORMATION OF A STATEMENT SUCH THAT IT WILL BE THE OPPOSITE OF ITS TRUTH VALUE.
NEGATION
a statement refers to whether it is theoretically true or theoretically false
Truth value
type of statement that just reverses the order of a conditional statement. The conclusion q becomes the hypothesis and the hypothesis p becomes the conclusion. It is the if q , then p statement.
CONVERSE
type of statement that negates both the hypothesis and conclusion.
Inverse
type of statement that just reverse the order of an INVERSE statement.
Contrapositive
give the SYMBOLISM of the 5 types of statements
Conditional:
- p -> q
Converse:
- q -> p
Inverse:
- ~p -> ~q
Contrapositive:
- ~q -> p
Biconditional:
- p <–> q
“If an animal barks, then it is a dog.” turn this statement into converse.
If it is a dog, then it barks.
“If it is a kite, then it flies.” turn this statement into converse.
If it flies, then it is a kite.
“If two lines are parallel, then their slopes are equal.” turn this statement into inverse.
If two lines are NOT parallel, then their slopes are NOT equal.
“If two lines are parallel, then their slopes are equal.” turn this statement into contrapositive.
If two slopes are NOT equal, then the lines are not parallel.
“If I will do regular exercise, then I will be physically fit.” turn this statement into a biconditional.
I do regular exercise if and only I am physically fit (can be interchanged)
There will be a test in Mathematics tomorrow. Give the negation of the given statement.
There will be no test in Mathematics tomorrow.
There is PE subject in the Senior High School. Give the negation of the given statement.
There is no PE subject in the Senior High School.
A right angle measures exactly 90 degrees. Give the subject and predicate.
Subject: A right angle
Predicate: measures exactly 90 degrees
Parallel lines do not intersect no matter how far they are extended. Give the subject and predicate.
Subject: Parallel lines
Predicate: do not intersect no matter how far they are extended
