Geometry Test #2 Flashcards
Conjunctions
“And” ; Ʌ
Only true when BOTH statements are true.
Disjunctions
“Or” ; V
Only true when AT LEAST one statement is true.
Negation
Not the original statement:
Statement: p
Negation: ~p
~(~aVb) = aɅ~b
~(p → ~q) = ~p → q
Conditional Statements
aka. (If-Then Statements)
If p, then q Symbol Notation: p→q
Hypothesis, Conclusion
True for everything EXCEPT:
T → F = F
Biconditional Statements
“If and only if”:
p → q
q → p
———
p ↔ q
Inverse
Inverse = OPPOSITE of the conditional
Conditional: p → q
Inverse: ~p → ~q
Converse
Interchange the hypothesis and conclusion:
Conditional: If p, then q ; p → q
Converse: If q, then p ; q → p
What two things are logically equivalent to one another?
The CONVERSE and INVERSE.
Contrapositive
Negate the terms of a converse:
Conditional: p → q
Converse: q → p
Contrapositive: ~q → ~p
What two things are logically equivalent to one another?
The CONDITIONAL and CONTRAPOSITIVE
Truth Table
Tautology
When all ending values of the truth table are true.
Law of Detachment
Removing the 2nd:
1st→2nd, therefore 2nd
Law of the Contrapositive
Finding the contrapositive of the conditional//premise
p→q therefore ~q→~p
Modus Tollens
Negatives of both values
p→q and ~q = ~p
