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sara12345

  • 2 years ago

Logic

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  1. sara12345
    • 2 years ago
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    |dw:1348907509327:dw|

  2. sara12345
    • 2 years ago
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    if 'a', then 'b' : a-> b

  3. sara12345
    • 2 years ago
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    is that correct ?.. can i write teh same as, only if 'b', then 'a' ?

  4. badreferences
    • 2 years ago
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    Are you asking if you can reverse "if A, then B" to "if B, then A"?

  5. sara12345
    • 2 years ago
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    no, the thing troubling me is "only if"

  6. badreferences
    • 2 years ago
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    That doesn't sound right. "Only if" B still has many things that aren't A.

  7. sara12345
    • 2 years ago
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    actually i dont get "if and only if", im trying to understand it by breaking it down to "if" and "only if"

  8. sara12345
    • 2 years ago
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    may i knw why it doesnt sound right to you, it does sound right to me

  9. badreferences
    • 2 years ago
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    But... a square is a kind of a rectangle.

  10. sara12345
    • 2 years ago
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    |dw:1348907860375:dw|

  11. badreferences
    • 2 years ago
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    "A square cannot be a rectangle"?

  12. sara12345
    • 2 years ago
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    excuse me, my question is different, plz look at the diagram what im asking

  13. sara12345
    • 2 years ago
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    only if its b, then only it can be a

  14. UnkleRhaukus
    • 2 years ago
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  15. badreferences
    • 2 years ago
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    "In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles." "In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles (90-degree angles, or right angles)." So a square shares all the properties of a rectangle, but has the additional condition that it's regular. So all squares are rectangles.

  16. sara12345
    • 2 years ago
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    a doesnt have any possibility outside b

  17. badreferences
    • 2 years ago
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    No, but just because it's B doesn't necessarily mean it's A.

  18. badreferences
    • 2 years ago
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    Replace A with "it rained last night" and B with "the grass was wet the next morning".

  19. badreferences
    • 2 years ago
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    There are many ways for the grass to be wet the next morning (dew, sprinklers), even if it raining last night necessarily means that the grass is wet next morning.

  20. sara12345
    • 2 years ago
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    @UnkleRhaukus you got me correctly! 3rd point in ur snapshot says it

  21. badreferences
    • 2 years ago
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    Ahh, okay, the third point. I thought you were saying something else. My bad.

  22. sara12345
    • 2 years ago
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    its okay... i dont get "if and only if" could you walk me through slowly plz

  23. sara12345
    • 2 years ago
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    ive understood "only if" i guess, whats "if and only if", i mean i knw it means, a iff b is same as a->b, b->a

  24. sara12345
    • 2 years ago
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    but why it is called "if and only if" is confuses me

  25. UnkleRhaukus
    • 2 years ago
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    \[\begin{array}{ccccc}\phi&\psi&\phi\Rightarrow\psi&\phi \Leftarrow\psi&\phi\Leftrightarrow\psi\\ \hline \\T&T&T&T&T\\T&F&F&T&F\\F&T&T&F&F\\F&F&T&T&T\end{array}\]

  26. badreferences
    • 2 years ago
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    Unkle, is it just me, or is "only if B then A" different from "A iff B"?

  27. badreferences
    • 2 years ago
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    only if B then A is different from A if and only if B.

  28. sara12345
    • 2 years ago
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    im familiar with xnor truth table, but still why its called "if and only if" should we break it into two : 1) if, 2) only if

  29. sara12345
    • 2 years ago
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    a iff b break as : if a then b, a only if b ?

  30. zzr0ck3r
    • 2 years ago
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    @sara12345 do you understand if a then b?

  31. UnkleRhaukus
    • 2 years ago
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    if and only if \(\Leftrightarrow\) iff

  32. sara12345
    • 2 years ago
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    yes, i understood iff also, only the "phrase" is confusing me

  33. zzr0ck3r
    • 2 years ago
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    I think I'm confused about what your asking. Sorry.

  34. sara12345
    • 2 years ago
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    sorry, like a iff b can i break it into 2 pieces : 1) if a then b, 2) a only if b ?

  35. sara12345
    • 2 years ago
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    the two broken statements, do they cover completely "a iff b" ?

  36. sara12345
    • 2 years ago
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    il start over.

  37. UnkleRhaukus
    • 2 years ago
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    these statements say the same thing 1) if a then b, 2) a only if b _______

  38. sara12345
    • 2 years ago
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    ohh yea they say same thing, a->b

  39. UnkleRhaukus
    • 2 years ago
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    to meant the same as a iff b switch the letters around in one of them

  40. sara12345
    • 2 years ago
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    so hw can iu break it meanigfully

  41. sara12345
    • 2 years ago
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    a "if and only if " b : a <--> b a "if" b : b->a a "only if" b : a->b i guess now i have it working in above

  42. sara12345
    • 2 years ago
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    i see there is lot of difference between, "if" and "only if"

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