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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

Comments for Symbolic Arguments

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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


Feb 15, 2017
Logic NEW
by: Anonymous

Either organic chemistry or genetics is the most difficult science at culver Stockton college. Organic chemistry is the most difficult science course at the college only if it's GPA course is lower than that of genetics. However, this is not the case. It follows that genetics is the most difficult science course at C-SC.

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