Math Case

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

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