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Symbolic Arguments











































if the canteen is full, then we can go for a walk.
we can go for a walk and we will not get thirsty.
if we go for a walk, then the canteen is not full.



A)translate the argument into symbolic form.
B)determine if the argument is valid or invalid

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Oct 05, 2011
Symbolic Arguments
by: Staff


Question:

if the canteen is full, then we can go for a walk.
we can go for a walk and we will not get thirsty.

therefore, if we go for a walk, then the canteen is not full.



A)translate the argument into symbolic form.
B)determine if the argument is valid or invalid



Answer:

∧: “and”symbol
∨: “or” symbol
~: “negation” (not) symbol


A)translate the argument into symbolic form.

p = canteen is full
q = we can go for a walk
r = get thirsty

p → q

q ∧~r



B)determine if the argument is valid or invalid

[(p → q) ∧(q ∧~r)] → ~ p

Argument is invalid. See row 2 of truth table.


All possible combinations of p, q, and r are shown in the following Truth Table. There are 8 possible combinations (2³ = 8):

......p.......q........r........~r........(q∧~r )

1....T......T........T........F........F
2....T......T........F........T........T
3....T......F........T........F........F
4....T......F........F........T........F
5....F......T........T........F........F
6....F......T........F........T........T
7....F......F........T........F........F
8....F......F........F........T........F


Thanks for writing.

Staff
www.solving-math-problems.com


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