Logic of Compound Statements

Assignment 1, reading page 1 in list

Order of Operations

Negation, Conjunction/Disjunction, Parentheses(override)

Disjunction

OR

Negation

NOT

Conjunction

AND

Negation

~p; not p; it is not the case that p

Conjunction

p ∧ q; p and q

Disjunction

p ∨ q; p or q

Exclusive or

p ⊕ q; Either p or q(but not both)

The opposite of Identity Law is…

Universal Bound Law

Other Terms for AND

But, however

Which Law sends negations throughout the parentheses?

Tautology

A statement that is always True

Contradiction

A statement that is always false

A proposition is also called

a statement

Does a proposition always have to be true?

No

What kind of sentences can NOT be Propositions?

Questions; commands; Fragments/nonsense; ambiguous pronouns

The negation of less than is

greater than or equal to

How many rows in a Truth table

2ⁿ , with n being how many variables

Commutative Law

• p ∨ q ≡ q ∨ p

• p ∧ q ≡ q ∧ p

Associative Law

• (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

• (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

Distributive La

• p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

• p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Identity Law

• p ∨ c ≡ p

• p ∧ t ≡ p

Negation Law

• p ∨ ¬p ≡ t

• p ∧ ¬p ≡ c

Double Negation Law

• ¬(¬p) ≡ p

Idempotent Law

• p ∨ p ≡ p

• p ∧ p ≡ p

Universal Bound Law

• p ∨ t ≡ t

• p ∧ c ≡ c

De Morgan’s Law

• ¬(p ∨ q) ≡ ¬p ∧ ¬q

• ¬(p ∧ q) ≡ ¬p ∨ ¬q

Absorption Law

• p ∧ (p ∨ q) ≡ p

• p ∨ (p ∧ q) ≡ p

Negation of tautology and contradiction

• ¬t ≡ c

• ¬c ≡ t