Question

is the inference pattern given below valid ??
(p^q)->~t
w v r
w->p
r->q

Answer 1

w->p
r->q
...
w v r
............from the principle of constructive dilemma..... they can be written in single..as . p v q.......
........
but how to solve...
(p^q)->~t
p v q.......

Answer 2

the final conclusion given is.........(w v r)->~t

Answer 3

i wish i could help on it, but quite frankly, i wouldnt know where to begin with it :/

Answer 4

how much of it are you sure about?

Answer 5

i'm sure about......
the last three.....
and by simplifying them........
i got..
p v q....
so..we have to solve (p^q)->~t and p v q.....
and check whether if it is equal to......(w v r)->~t

Answer 6

would truth tables be helpful?

and is this one big logical expression:

((p^q)->~t) ^ (p v q) to solve?

Answer 7

but i'm not allowed to use truth tables here...

:(

Answer 8

do they stab you in the eye as well so that you have to work with impaired vision too??

Answer 9

if using truth tables gets you to the results, then you have something to work with to guide you

Answer 10

with any luck im remembering these correctly

p q t p^q -> -t
1 1 1 1 0 =0
1 1 0 1 1 =1
1 0 1 0 0 =1
1 0 0 0 1 =1
0 1 1 0 0 =1
0 1 0 0 1 =1
0 0 1 0 0 =1
0 0 0 0 1 =1

w r t wvr ->-t
1 1 1 1 0 =0
1 1 0 1 1 =1
1 0 1 1 0 =0
1 0 0 1 1 =1
0 1 1 1 0 =0
0 1 0 1 1 =1
0 0 1 0 0 =1
0 0 0 0 1 =1

Answer 11

i think you should begin with truth table.

Answer 12

i see i didnt include the ^ (pvq) tho

Answer 13

so........ is it an invalid inference pattern??

Answer 14

w->p (one case false)
r->q (one case false)
w^r (one case true)
w or r (one case false)

Answer 15

pvq has the same design as wvr soo

^ compared to
0 1 =0 0
1 1 =1 1
1 1 =1 0
1 1 =1 1
1 1 =1 0
1 1 =1 1
1 0 =0 1
1 0 =0 1

without knowing anything else, my gut tells me that since the patterns are different, then we cannot infer it

Answer 16

experiment tho seems to have a better grasp on what its asking for tho :)

Answer 17

plz.......... try to solve without using truth tables..

Answer 18

it is an ivalid inference .....it seems...
let's leave it....
@experimentX @amistre64 thanks a lot.......