Question

Show that the statement (~p V q) ʌ (p ʌ ~ q) is a logical contradiction by any means.

Answer 1

Hey Miss Kelsey :)
Hmmmm....

Answer 2

There is some property that will lead us to this implication, yes? :o
\(\Large\rm p\wedge\text{~}q \implies p\)
If we have p, and we don't have q, then we have .... p.

Answer 3

Likewise we could do something with the first,
\(\Large\rm \text{~}p\vee q\implies \text{~}p\)

We have q OR we don't have p, so in both cases, we don't have p.

Answer 4

It's been too long :)
I don't remember the names of all of the rules lol

Answer 5

But anyway, that would lead us to \(\Large\rm \text{~}p\wedge p\)
ya? :)

Answer 6

Do you know what a logical contradiction is exactly? I have this question for my online math class but the definition is no where to be found in my textbook @zepdrix

Answer 7

Because I honestly have no clue what you wrote relates to that lol

Answer 8

If we can get to `~p` `ʌ` `p`,
written out in words this looks like,
`not p` `and` `p`

We're assuming p cannot be both true and false at the same time.
So this is a contradiction, it doesn't make any sense.
We cannot have p and, no p, at the same times.

I was taking these grey parts: `(~p V q)` ʌ `(p ʌ ~ q)`
and was trying to show that the first box is equivalent to `~p`
while the second box is equivalent to `p`

Answer 9

So I was trying to show that this:
`(~p V q)` ʌ `(p ʌ ~ q)`
is logically equivalent to this:
`~p` ʌ `p`
And in this form we can more clearly see the contradiction in it.

Answer 10

Too confusing? :o
Brain esplode?

Answer 11

Definite brain explosion but thank you for breaking it down like that. It definitely makes more sense now!

Answer 12

np :)
Darn, I can't find my old book, was going to look for a more formal definition. oh well