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Math Help - [SOLVED] Boolean Simplification

  1. #1
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    [SOLVED] Boolean Simplification

    Hi guys,

    I've tried to simplify a formula, and I'm not sure if I've done it right. The following is my solution - I've indicated which logic rule(s) I've used to arrive at each line (excuse the rubbish handwriting):

    http://www.zaraphrax.net/~fagg/boolean_mhf.jpg

    Any guidance is appreciated.

    Thanks!
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  2. #2
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    Bratislava
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    Quote Originally Posted by Ashgasm View Post
    Hi guys,

    I've tried to simplify a formula, and I'm not sure if I've done it right. The following is my solution - I've indicated which logic rule(s) I've used to arrive at each line (excuse the rubbish handwriting):

    http://www.zaraphrax.net/~fagg/boolean_mhf.jpg

    Any guidance is appreciated.

    Thanks!
    I think that your solution is ok. You may notice that the last line is in fact p\Rightarrow q.

    You can also use truth table to verify that your answer is correct.
    For proposition which have the form of implication there is a shorter way:
    Clearly p\Rightarrow q if false only in one case: p=1, q=0.
    Let us try to the same thing with the first expression
    [p\land \neg(p\Rightarrow q)] \Rightarrow q.
    This implication is false only if [p\land \neg(p\Rightarrow q)]=1 and q=0. For a conjunction to be true, you need that both of the operands are true. This means that p=1, and \neg(p\Rightarrow q) is also true for p=1,q=0.
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  3. #3
    Junior Member
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    Quote Originally Posted by kompik View Post
    I think that your solution is ok. You may notice that the last line is in fact p\Rightarrow q.

    You can also use truth table to verify that your answer is correct.
    For proposition which have the form of implication there is a shorter way:
    Clearly p\Rightarrow q if false only in one case: p=1, q=0.
    Let us try to the same thing with the first expression
    [p\land \neg(p\Rightarrow q)] \Rightarrow q.
    This implication is false only if [tex][p\land \neg(p\Rightarrow q)]=1[/math and q=0.
    Kompik,

    Thanks for your reply. Much appreciated.
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