Finding truth value of each propositional variable.

[sunny79]

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

 

[BvU]

I started by substituting T in all variables...

That is not a good start. All you are given is that [p^(qVr)]^ ~r = T !

 

[WWGD]

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.

 

[BvU]

Giving it away, eh

 

[sunny79]

Notice in an /\ sentence, both components must be true. That simplifies it a bit.

Gotcha! Thanks. :)