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Math Help - Help with logic problem

  1. #1
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    Question Help with logic problem

    I need to solve the following problem:

    Formalize the follwing sentences as logical sentences.

    If its not raining I walk to work but if itīs raining i drive to work.
    I dont drive to work if itīs not raining.
    If dirve to work itīs raining but i walk to work if itīs not raining.

    The following designations are to be used.
    p= itīs raining
    q= I walk to work
    r= I drive to work

    Please help me understand.
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  2. #2
    Member kjchauhan's Avatar
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    Quote Originally Posted by Monika1987 View Post
    I need to solve the following problem:

    Formalize the follwing sentences as logical sentences.

    If its not raining I walk to work but if itīs raining i drive to work.
    I dont drive to work if itīs not raining.
    If dirve to work itīs raining but i walk to work if itīs not raining.

    The following designations are to be used.
    p= itīs raining
    q= I walk to work
    r= I drive to work

    Please help me understand.
    (\sim P \Rightarrow Q) \cup (P \Rightarrow R)

    \sim R \Rightarrow \sim P

    (R \Leftarrow P) \cup (Q \Leftarrow \sim P)

    Now simplify..
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  3. #3
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    Quote Originally Posted by Monika1987 View Post
    I need to solve the following problem:

    Formalize the follwing sentences as logical sentences.

    If its not raining I walk to work but if itīs raining i drive to work.
    I dont drive to work if itīs not raining.
    If dirve to work itīs raining but i walk to work if itīs not raining.

    The following designations are to be used.
    p= itīs raining
    q= I walk to work
    r= I drive to work

    Please help me understand.
    The formalization is as follows :

    1) if it is not raining i walk to work : \neg p\rightarrow q

    2) if it is raining i drive to work :  p\rightarrow r

    3) i do not drive to work if it is not raining : \neg p\rightarrow\neg r

    4) if i drive to work it is not raining :  r\rightarrow\neg p

    5) I walk to work if it is not raining : \neg p\rightarrow q

    (1) and (5) are the same
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