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Homework 3. True or False?. True or false? For each of the following WFFs, determine whether it is true or false on the given evaluation. Evaluation : P = T, Q = T, R = T 1 . ~(P ↔ Q) 2. ~((P v (Q → R)) & ~P). True or False?.
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True or False? True or false? For each of the following WFFs, determine whether it is true or false on the given evaluation. Evaluation: P = T, Q = T, R = T 1. ~(P ↔ Q) 2. ~((P v (Q → R)) & ~P)
True or False? True or false? For each of the following WFFs, determine whether it is true or false on the given evaluation. Evaluation: P = T, Q = T, R = T 1. ~(P ↔ Q) 2. ~((P v (Q → R)) & ~P)
True or False? True or false? For each of the following WFFs, determine whether it is true or false on the given evaluation. Evaluation: P = T, Q = T, R = T 1. ~(P ↔ Q) 2. ~((P v (Q → R)) & ~P)
From My Inbox Dear Michael, Are there too many or too little parentheses in this formula: ~((P v (Q → R)) & ~P) Thanks, --Concerned Student
Nope! ~((P v (Q → R)) & ~P)
Set #1 ~((P v (Q → R)) & ~P)
Set #2 ~((P v(Q → R)) & ~P)
Set #3 ~((P v(Q → R))& ~P)
Definition of WFF • All sentence letters are WFFs. • If φ is a WFF, then ~φ is a WFF. • If φ and ψ are WFFs, then (φ & ψ), (φ v ψ), (φ → ψ), (φ ↔ ψ) are also WFFs. • Nothing else is a WFF.
Demonstration Using the definition we can show that certain sequences of symbols are WFFs. For example ~((P v (Q → R)) & ~P) is a WFF.
All Sentence Letters Are WFFs By (i), all sentence letters are WFFs. So: P is a WFF Q is a WFF R is a WFF
All Sentence Letters Are WFFs By (i), all sentence letters are WFFs. So: P is a WFF Q is a WFF R is a WFF
All Sentence Letters Are WFFs By (i), all sentence letters are WFFs. So: P is a WFF Q is a WFF R is a WFF
All Sentence Letters Are WFFs By (i), all sentence letters are WFFs. So: P is a WFF Q is a WFF R is a WFF
Scope Every occurrence of a connective in a WFF has a scope. The scope of that occurrence is the smallest WFF that contains it. For example The scope of “&” in “(~(~P&Q)→P)” is (~P&Q) • (~(~P & Q) → P) is not a WFF. • (~(~P & Q) → P)is not a WFF. • (~(~P & Q) → P) is a WFF, but is bigger than (~P&Q)
Occurrences Notice that the same symbol can occur different times in the same formula, and that its different occurrences can have different scopes. • ~((~P & Q) & (R ↔ Q)) • ~((~P & Q) & (R ↔ Q)) • ~((~P & Q) & (R ↔ Q)) • ~((~P & Q) & (R ↔ Q))
Scope of → ~((P v(Q → R))& ~P)
Scope of v ~((P v(Q → R))& ~P)
Scope of & ~((P v(Q → R))& ~P)
Scope of Main Connective ~((P v(Q → R))& ~P)