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Muzic44

  • 2 years ago

Could someone please help me with this question? Anyone? :c Read the two statements shown below. If the weather is not cold, Meg will go swimming. The weather is cold, or Meg will go swimming. Create truth tables for the logical form of the two statements (not to be submitted). Use the truth tables to determine whether the two statements are logically equivalent. Justify your answer.

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  1. Muzic44
    • 2 years ago
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    @Hero pwease help...

  2. Muzic44
    • 2 years ago
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    @jim_thompson5910

  3. jim_thompson5910
    • 2 years ago
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    do you know how to create truth tables?

  4. Muzic44
    • 2 years ago
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    Somewhat... Thats with all the odd symbols right?

  5. jim_thompson5910
    • 2 years ago
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    not sure what you mean by "Thats with all the odd symbols", but go ahead and make one and post it here so we can see it

  6. Sujay
    • 2 years ago
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    No, because she can go swimming and the weather can be cold. The first statement only guarantees swimming if the weather isn't cold. It doesn't put away the possibility of her going swimming in cold weather.

  7. Muzic44
    • 2 years ago
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    @jim_thompson5910 I have no idea what I'm doing sorry.

  8. Muzic44
    • 2 years ago
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    @Sujay But how to you justify that? Just by looking at it and logically processing it?

  9. jim_thompson5910
    • 2 years ago
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    ok I'll start you off let p: The weather is cold q: Meg will go swimming So start off |dw:1355618416718:dw|the truth table to get

  10. jim_thompson5910
    • 2 years ago
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    |dw:1355618482901:dw|

  11. jim_thompson5910
    • 2 years ago
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    |dw:1355618539480:dw|

  12. jim_thompson5910
    • 2 years ago
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    |dw:1355618570286:dw|

  13. Muzic44
    • 2 years ago
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    Could you explain what all that means? O _ O

  14. jim_thompson5910
    • 2 years ago
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    so that's the truth table for ~p -> q which is the translation of "If the weather is not cold, Meg will go swimming."

  15. jim_thompson5910
    • 2 years ago
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    you start off with P and Q and you fill out the first column to be T, T, F, F then you do T, F, T, F for the second column this basically sets up all the possible truth value pairings for P and Q

  16. Leo-SMI
    • 2 years ago
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    |dw:1355618581504:dw|

  17. jim_thompson5910
    • 2 years ago
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    then you fill out the ~P column by flipping everything you see in the P column

  18. Muzic44
    • 2 years ago
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    This is probably a stupid question but how come there are 4 in each column?

  19. jim_thompson5910
    • 2 years ago
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    because there are 2^2 = 4 ways to have truth values for P and Q when they pair up

  20. jim_thompson5910
    • 2 years ago
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    TT TF FT FF

  21. Muzic44
    • 2 years ago
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    OH!

  22. jim_thompson5910
    • 2 years ago
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    finally, you fill out the ~P -> Q column by only writing F if ~P is true and Q is false otherwise, its true by default

  23. Leo-SMI
    • 2 years ago
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    TT TF FT FF

  24. Muzic44
    • 2 years ago
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    Hold on I kinda forgot the question

  25. Muzic44
    • 2 years ago
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    How do we figure out if its logically equilvalent? Do I just for whichever statement makes sense in that table?

  26. jim_thompson5910
    • 2 years ago
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    make a truth table for the second statement "The weather is cold, or Meg will go swimming"

  27. jim_thompson5910
    • 2 years ago
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    and compare the truth values in the last column

  28. Sujay
    • 2 years ago
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    Ya Muzic, that is what I did--something I learned in Geometry.

  29. Muzic44
    • 2 years ago
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    ???

  30. Muzic44
    • 2 years ago
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    how did you guys make that table? IS there like a tool or something?

  31. jim_thompson5910
    • 2 years ago
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    I used the draw feature

  32. jim_thompson5910
    • 2 years ago
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    under the text box is the draw button

  33. Muzic44
    • 2 years ago
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    Oh sorry I'm stupid -_-

  34. Muzic44
    • 2 years ago
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    Okay this is probably wrong but

  35. jim_thompson5910
    • 2 years ago
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    no worries and you're not

  36. Muzic44
    • 2 years ago
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    |dw:1355619318974:dw|

  37. Muzic44
    • 2 years ago
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    ... D:

  38. jim_thompson5910
    • 2 years ago
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    I'll make a blank table for you to fill out

  39. Muzic44
    • 2 years ago
    Be