Math Case
Essay by Paul • May 16, 2012 • Case Study • 393 Words (2 Pages) • 1,655 Views
Operation Symbol How Operation Works
Negation ~P (Not P) Make T/F opposite
Disjunction P Λ Q (And) Only true when both claims are true
Conjunction P V Q (Or) Only false when both claims are false
The Conditional P → Q (If P, then Q) When P is True and Q is False, P → Q is False
The Biconditional P ↔ Q (P if and only if Q) True when both claims are either true or false
( ) It is the case that
Truth Table 2^n =Number of rows in a truth table
P Q P Λ Q (And) P V Q (Or) P → Q (If P, then Q) P ↔ Q (P if and only if Q)
T T T T T T
T F F T F F
F T F T T F
F F F F T T
3. Order of Operations: a. Parenthesis b. Negation c. Other Operations
1. Ex: ~[(~P Λ ~Q) V~Q] ; P= F ~[(T Λ F) V F] ; Q= T ~[F V F] = ~F = T
a. Demorgans Laws (Negation Laws): Negation is distributed, And always negates to Or, Or to And
P Q (P Λ Q) ~(P Λ Q) ~P ~Q ~P V ~Q
T T T F F F F
T F F T F T T
F T F T T F T
F F F T T T T
Argument: Systematic presentation of your case
P. You finish the test early, Q. You can leave early
P → Q a. Go to column P → Q and cross out all False claims
Q . b. Go to column Q and cross out all False Claims
P c. Circle what's left if column P
1. If it is all True, then claim is Valid
2. If it is false, or true and false, claim is invalid
P Q P →Q
T T T
T F F
F T T
F F T
Quantifiers: 1st statement tells us what to write in diagram, 2nd where to place letter, if letter inside graph=valid
1. Universal (): All: every element of the group has this property
2. Existential (: Some: Some of the elements of the group has this property
All sophomores have earned at least 60 credits
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