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Math Help - Finding the truth value

  1. #1
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    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 ?

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  2. #2
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    Re: Finding the truth value

    Quote Originally Posted by Mhmh96 View Post
    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 View Post
    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.
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  3. #3
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    Re: Finding the truth value

    But we should use the given statements ,to determine the truth value of B, right ?
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  4. #4
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    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?
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  5. #5
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    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
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  6. #6
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    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.
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  7. #7
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    Re: Finding the truth value

    I agree.
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