Finding truth value of each propositional variable.

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The discussion focuses on finding the truth values of propositional variables in the expression [p^(qVr)]^ ~r, assuming it is true. The initial approach involved substituting True for all variables, leading to a conclusion that p and q are True while r is False. However, it was pointed out that this method is flawed since the expression must hold true under the given conditions. The importance of ensuring both components in an "and" statement are true is emphasized, which simplifies the evaluation. The conversation highlights the need for careful consideration of logical structures when determining truth values.
sunny79
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Homework Statement
Assume that the compound statement is true. Find the truth value of each propositional variable.
Relevant Equations
[p^(qVr)]^ ~r
Note:
^ represents and.
V represents or
~ represents not
T represents True
F represents False

My solution...

I started by substituting T in all variables...

[p^(qVr)]^ ~r
[T^(TVT)] ^ ~T
(T^T) ^ F
T^F
F
The answer is p = True q = True r = False
 
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sunny79 said:
I started by substituting T in all variables...
That is not a good start. All you are given is that [p^(qVr)]^ ~r = T !
 
sunny79 said:
Homework Statement: Assume that the compound statement is true. Find the truth value of each propositional variable.
Homework Equations: [p^(qVr)]^ ~r

Note:
^ represents and.
V represents or
~ represents not
T represents True
F represents False

My solution...

I started by substituting T in all variables...

[p^(qVr)]^ ~r
[T^(TVT)] ^ ~T
(T^T) ^ F
T^F
F
The answer is p = True q = True r = False
Notice in an /\ sentence, both components must be true. That simplifies it a bit.
 
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Giving it away, eh :wink:
 
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WWGD said:
Notice in an /\ sentence, both components must be true. That simplifies it a bit.

Gotcha! Thanks. :)
 
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