Unit two Flashcards
Conditional statements
most often a if then statement, shows a hypothesis and a conclusion. p→q, if p then q, hypothesis → conclusion, equivalent to contrapositive
Negation
the negation of a statement is the opposite of that statement. Ex. The ball is red, the negation of this is the ball is not red.
Converse
swap the hypothesis and the conclusion, so the statement becomes q→p equivalent to inverse
Inverse
negating both the hypothesis and conclusion so the statement becomes ~p~q equivalent to converse
contrapositive
fist writes the converse, and then negates both the hypothesis and conclusion so the statement becomes ~p→~q a combination of converse and inverse equivalent to conditional statements.
Biconditional statements
when a conditional statement and its converse are both true, you can write them as a single biconditional statement. These statements always contain the words, “if and only if”
Linear pair postulate
if two angles form a linear pair then they are congruent
definition of perpendicular lines
if two lines are perpendicular then they intersect at a 90 degree angle
Inductive reasoning
patterns and what comes next, basically common sense
Deductive reasoning
what can you conclude? what logic did you use? process that people use to make decisions and solve problems
Law of detachment
If the conditional statement is true and the hypothesis is true, then the conclusion will be true as well.
transitive property of equality
if a=b and b=c then a=c
symmetric property of equality
This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement.
reflexive property of equality
the same thing equals the same thing a=a
