Unit 2 Flashcards
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Inductive reasoning
reasoning that uses a number of examples to arrive at a conclusion
conjecture
educated guess that is derived from inductive reasoning
counterexample
an example that shows a conjecture is False
Negation
A negation of a statement has the opposite truth value
shows by -p
conditional statement
A statement that can be written in if-then form
ex: p—->q
includes hypothesis + conclusion
Inverse
formed by negating the hypothesis and conclusion
-p —-> -q
Converse
Formed by switching the hypothesis and conclusion
Symbolic form= if q ———-> p
Contrapositive
Formed by negating and switching the hypothesis and conclusion
symbolic form= -q —–> -p
Equivalent statements
When two statements are both true or false
Which statements are logically equivalent
conditional and contrapositive
Which statements are logically equivalent when false
converse and inverse
Bi-conditional statements
The Conjunction of a conditional and it’s converse
Symbolic form of a bi-conditional
p <—-> q
When can you write a bi-conditional statement
when conditional and converse are true
Deductive reasoning
Using
facts
definitions
properties
laws of logic
to form a conjecture
Law of Detachment
If the hypothesis is true, then the conclusion is true
Law of Syllogism
Allos you to drow a conclusion from 2 conditional statements in which the conclusion of the first statement is the hypothesis of the 2nd statement
p-q
q-r
p-r
Addition Property of = def.
if a=b, then a+c = b+c
Subtraction property of equality
if a=b, then a -c = b - c
Multiplication prop of equality
if a=b, then ac=bc
Division prop of equality
If a=b + is not 0, then a/c=b/c
Substitution prop of equality
If a=b then a may be replaced by b in any expression or equation
What is substitution useful for
for values
Reflexive prop
a=a
