Chapter 2 Test Flashcards
(33 cards)
Hypothesis p and conclusion q (if/then)
Conditional statement
Opposite of the original statement
Negation
Exchange hypothesis and conclusion. If q, then p.
Converse
Negate hypothesis and conclusion. If not p, then not q.
Inverse
First write the converse, then negate both the hypothesis and conclusion. If not q, then not p.
Contrapositive
When 2 statements are both true or both false
Equivalent statements
A statement that contains the phrase “if and only if”
Biconditional statement
Unproven statement based on observations
Conjecture
When you find a pattern in specific cases then write a conjecture for a general case
Inductive reasoning
Specific case when the conjecture is false
Counterexample
Uses facts, definitions, accepted properties, and they las of logic to form a logical argument
Deductive reasoning
Law of detachment
If the hypothesis of a true conditional statement is true, then the conclusion is also true
A=B B=C A=C (laws of logic)
Law of syllogism
a=b a+c=b+c
Addition property of equality
A=b a-c=b-c
Subtraction property of equality
A=b ac=bc
Multiplication property of equality
A=b a/c=b/c
Division property of equality
A=b
Substitution property of equality
A+ (b+c)=(a+b)+c
A(bc)=(ab)c
Associative property
A+b=b+a
Ab+ba
Commutative property
A(b+c)=ab+ac
A(b-c)=ab-ac
Distributive property
A=a
Reflexive property of equality
A=b the b=a
Symmetric property of equality
A=b b=c
A=c
Transitive property of equality
