OpenStudy (ajprincess):

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

6 years ago
OpenStudy (jamesj):

First step: how do you write (p→q) as an logical expression that does not use the implication symbol → ?

6 years ago
OpenStudy (ajprincess):

|dw:1338105778405:dw|

6 years ago
OpenStudy (jamesj):

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

6 years ago
OpenStudy (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.

6 years ago
OpenStudy (ajprincess):

Nw I get t. when I take vq out I will get (~p^~r) which is equal to (~(pvr)vq)

6 years ago
OpenStudy (jamesj):

right

6 years ago
OpenStudy (ajprincess):

Thanxxxx a lot.

6 years ago