Use a truth table to determine whether the symbolic form of the argument is valid or invalid. p → q ~ p ———— ∴ ~ q See Picture

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 51E
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Use a truth table to determine whether the symbolic form of the argument is valid or invalid.

p → q
~ p
————
∴ ~ q

See Picture

T T
T F
F T
F F
TF
F F
TT
F
F
т
T
The argument is invalid.
T
F
F
T
p alp-a- p|(p )^~p~ q[ (p -q) ^~p]q
T T TF
T F
T
F
F F
FT FT
F F
F
The argument is valid.
F
T
FT
T
p qlp-a- p|(P q)~p- q|[ (p -q)^~p] -q
T T
T F
F T
F F
т
TF
F F
F
F
F
T
The argument is invalid.
F
F
T
p alp-a- p|(p –q)^~p|~ q[[ (p -q) ^~p] -~ q
T T TF
T F
FF
FT
F T
F F
F
F
T
The argument is valid.
F
F
т
F T
F
T
Transcribed Image Text:T T T F F T F F TF F F TT F F т T The argument is invalid. T F F T p alp-a- p|(p )^~p~ q[ (p -q) ^~p]q T T TF T F T F F F FT FT F F F The argument is valid. F T FT T p qlp-a- p|(P q)~p- q|[ (p -q)^~p] -q T T T F F T F F т TF F F F F F T The argument is invalid. F F T p alp-a- p|(p –q)^~p|~ q[[ (p -q) ^~p] -~ q T T TF T F FF FT F T F F F F T The argument is valid. F F т F T F T
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ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage