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Unit 2 - Logic, Reasoning and Proof (Final Exam Review)
Terms in this set (26)
Inductive reasoning means making conclusions based upon examples and patterns.
an unproven statement that is based on observations
a specific case for which a conjecture is false
an unproven statement that might be true and can be tested.
the part of a conditional statement that comes after "then."
a logical statement that has two parts, the hypothesis and the conclusion.
the opposite of the original statement.
created when the hypothesis and conclusion are reversed.
take the negation of the both the hypothesis and conclusion.
switch the if and then statements and negate each of them also.
is true IF AND ONLY IF the conditional and converse statements are BOTH TRUE.
uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.
Law of Detachment
if p→q is true, and p is true, then q is true.
Law of Syllogism
If p→q and q→r are true, then p→r is true.
Addition Property of Equality
If a=b, then a+c=b+c
Subtraction Property of Equality
If a = b, then a - c = b - c
Multiplication Property of Equality
If a = b, then ac = bc
Division Property of Equality
if a = b and c is not equal to 0, then a÷c = b÷c
Substitution Property of Equality
If a=b, then a can be substituted for b in any equation or expression
a(b + c) = ab + ac
a method to prove statements using properties that justify each step
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b, then b = a
Transitive Property of Equality
If a = b and b = c, then a = c
Congruent Complements Theorem
Angles complementary to the same angle or two congruent angles are congruent.
Congruent Supplement Theorem
Angles supplementary to the same angle or two congruent angles are congruent.
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