# Finding truth value of each propositional variable.

• sunny79
In summary, the given compound statement is true and after substitution of T in all variables, p = True, q = True, and r = False.
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

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.

sunny79
Giving it away, eh

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

Gotcha! Thanks. :)

WWGD

## What is the definition of a propositional variable?

A propositional variable is a symbol or letter that is used to represent a statement in propositional logic. It can take on the value of either true or false.

## How do you find the truth value of a propositional variable?

The truth value of a propositional variable can be found by evaluating the statement it represents based on the given circumstances or logic rules. This can be done through logical reasoning or the use of truth tables.

## Can a propositional variable have more than two truth values?

No, a propositional variable can only have two truth values: true or false. This is because propositional logic is based on binary (two-valued) logic.

## What is the difference between a propositional variable and a propositional statement?

A propositional variable is a symbol or letter used to represent a statement, while a propositional statement is an actual statement that can be either true or false. A propositional variable is like a placeholder for a propositional statement.

## How are propositional variables used in real-world applications?

Propositional variables are used in various fields such as mathematics, computer science, and philosophy to represent and analyze logical statements. They are also used in programming and artificial intelligence to create conditional statements and make decisions based on logical rules.

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