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ajprincess

  • 2 years ago

plzzz help. prove (p→q)∧(r→q) = (pvr)→q

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  1. JamesJ
    • 2 years ago
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    First step: how do you write (p→q) as an logical expression that does not use the implication symbol → ?

  2. ajprincess
    • 2 years ago
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    |dw:1338105778405:dw|

  3. JamesJ
    • 2 years ago
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    ~pvq or ~(p^~q), right So, rewrite now both sides of your expression using this rule and see what you get.

  4. JamesJ
    • 2 years ago
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    (p→q)∧(r→q) = (~p v q) ^ (~r v q) -- (*) and (pvr)→q = (~(pvr) v q) -- (**) So you need now just to show the two right-hand side expressions of (*) and (**) are equivalent.

  5. ajprincess
    • 2 years ago
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    Nw I get t. when I take vq out I will get (~p^~r) which is equal to (~(pvr)vq)

  6. JamesJ
    • 2 years ago
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    right

  7. ajprincess
    • 2 years ago
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    Thanxxxx a lot.

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