1 is invalid. Counter example: c & !d
You can make the truth table yourself, just write out c d e and then under each letter go through all the combinations of true and false. Like this:
c d e
f f f
f f t
f t f
f t t
2 is invalid: !a & y
3 is invalid.
!s | a -> g
!s
therefore g
!g = m | p
since g, therefore !m & !p
Thus !p
You actually have to make a truth table per her instructions, but you'll get the same answer.
4 is valid
!(k | r)
!k & !r
(d -> a) -> r is the same as !r -> !(d -> a)
since !r therefore !(d -> a)
d & !a
!a -> b
therefore b
So we get: !r, !k, d, !a, b
b = !r, valid
This post was edited by russian on Dec 8 2015 11:23am