# Finding the truth value

• Jun 14th 2012, 03:56 AM
Mhmh96
Finding the truth value
If the truth value is true for the following statements :

A <---> B

A ⋁ B

G ---> ∼ D

D

What is the truth value of the statement B ?

• Jun 14th 2012, 04:31 AM
emakarov
Re: Finding the truth value
Quote:

Originally Posted by Mhmh96
If the truth value is true for the following statements :

Similar to how the value of x^2 + 3x - 5 is determined by the value of x, the truth values of these statements are determined by the truth values of the variables they contain.

Quote:

Originally Posted by Mhmh96
What is the truth value of the statement B ?

By B, do you mean a formula that consists of just one propositional variable B, or do you mean the second formula on your list, i.e., A ⋁ B? In any case, see the remark above.
• Jun 14th 2012, 06:59 AM
Mhmh96
Re: Finding the truth value
But we should use the given statements ,to determine the truth value of B, right ?
• Jun 14th 2012, 07:05 AM
emakarov
Re: Finding the truth value
I am sorry; I read the question wrong. I thought that you need to find the truth values of the first four statements.

If A \/ B is true, then A is true or B is true. In the second case, we know the truth value of B. What can you say in the first case taking into account that A <-> B is true?
• Jun 14th 2012, 07:06 AM
Mhmh96
Re: Finding the truth value
I mean to Consider the 3 possible cases (given that it's true) for A V B, and to use A <---> B to see what each case means for B
• Jun 15th 2012, 01:47 AM
Mhmh96
Re: Finding the truth value
I think i understand that now,the first statement means either both A and B are true, or both A and B are false. From the second statement, at least one of A or B is true. Therefore, both A and B must be true.
• Jun 15th 2012, 01:49 AM
emakarov
Re: Finding the truth value
I agree.