PHL245 first week

What does the following sentence look like in official notation? Q∧R∧S→Z

(((Q∧R)∧S)→Z) becuase () starts at the left side

Symbols for Sentential Logic

1. Symbols for atomic statements • Capital letters P-Z 2. Symbols for the logical connectives • ~→ ↔∧ ∨ 3. Symbols for organization • ( ), [ ]

Official Notation Rules

1. Use round brackets, ( ), around every binary connective 2. Never use brackets around unary connectives or atomic statements Official notation is unambiguous

contradiction

A sentence is a contradiction if it is always false, or it can never be true • It is raining AND not raining • "It is BLAH and not BLAH"

tautology

A sentence is a tautology if it is always true, or it can never be false • It is raining OR not raining • "It is BLAH or not BLAH"

Atomic Molecular

A statement that has no logical connectives has logical connectives

Not-well-formed vs Informal

Formal: (P->Q) Informal: P->Q These mean the same thing. Not-well-formed: PQ This doesn't mean anything. Also not-well-formed: (P)->(Q)

Is the following symbolic sentence in official notation, informal notation, or a not-well-formed formula? ~(P∧S→(R∨~(T↔Z)))

Informal It has no () between P and S. The official notation ((P^S)→(Rv(~T←→Z)))

Is the following argument valid or invalid? If taxes go up then property sales go down. Taxes did not go up. Therefore property sales did not go down.

Invalid this tells us nothing about what happens if taxes do not go up and so we cannot conclude anything from it. Taxes could stay the same (~P) and sales could still go down for some other reason

Is the following symbolic sentence in official notation, informal notation, or a not-well-formed formula? ((P∧Q∨R)→(S∧T))

Not-Well-Formed ∧ and ∨ are ambiguous

Is the following symbolic sentence in official notation, informal notation, or not well-formed? (P→(~Q∨(H∧S)))

not-well-formed because statements can only be represented with the letters P-Z. If you were to change the H to another letter withing P-Z then the sentence is then official.

A deductive argument is valid if

whenever the premises are true the conclusion must be true

Unary connective

~ negation