ajprincess
  • ajprincess
plzzz help. prove (p→q)∧(r→q) = (pvr)→q
Mathematics
katieb
  • katieb
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JamesJ
  • JamesJ
First step: how do you write (p→q) as an logical expression that does not use the implication symbol → ?
ajprincess
  • ajprincess
|dw:1338105778405:dw|
JamesJ
  • JamesJ
~pvq or ~(p^~q), right So, rewrite now both sides of your expression using this rule and see what you get.

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JamesJ
  • JamesJ
(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.
ajprincess
  • ajprincess
Nw I get t. when I take vq out I will get (~p^~r) which is equal to (~(pvr)vq)
JamesJ
  • JamesJ
right
ajprincess
  • ajprincess
Thanxxxx a lot.

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