7.4 Rules of Replacement II Trans, Impl, Equiv, Exp, Taut.
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Transcript of 7.4 Rules of Replacement II Trans, Impl, Equiv, Exp, Taut.
14. Transposition (Trans)
(P Q) :: (~Q ~P)
If Renée is a Californian then she is from the west coast. If she is not from the west coast, then she is not a
Californian.
P Q :: ~Q
~P
T T T T F T F
T F F T T F F
F T T T F T T
F T F T T T T
15. Impl
15. Material Implication (Impl)
(P Q) :: (~P v Q)
“If you bother me then I will punch you in the nose.”
“Either you stop bothering me or I will punch you in the nose.”
16. Equiv
16. Material Equivalence (Equiv)
(P Q) :: [(P Q) (Q P)]
“P iff Q” :: “if P then Q, and if Q then P”
(P Q) :: [(P Q) v (~Q ~P)]
“P iff Q” :: “P and Q are both true, or they are both false”
17. Exp
17. Exportation (Exp)
[(P Q) R] :: [P (Q R)]
“If we have P, then if we have Q we have R”
“If we have both P and Q, then we have R”
14. Trans (P Q) :: (~Q ~P)
15. Impl (P Q) :: (~P v Q)
16. Equiv (P Q) :: [(P Q) (Q P)]
17. Exp [(P Q) R] :: [P (Q R)]
18. Taut P :: P v PP :: P P
7.4.1 p. 52
Provide logically equivalent statements using the rules of replacement.
Do 1-10.
Do the evens if you were born on an even numbered day. Do odds if you were born on an odd numbered day.