Determine if the argument is valid.

[pingingjungle8]

Determine whether or not each of the following arguments is valid.

1.)

p ? ((¬q )? r)
¬(p ? s)
---------------------------
¬(s ?(q?(¬r)))

I think for this one I need to use De Morgan Law, but I'm really confused. . .

2.)

Either I wear a red tie or I wear blue socks.
I am wearing blue socks.
-----------------------------------------------------------------------------------------------
I am not wearing a red tie

I have attempted to make a truth table to prove that it is valid, but I think I am missing a row. Any suggestions?

p q p or q ~p
T| T| T| F|
T| F| T| F|
F| T| T| T|
F| F| F| T|

Thanks for any helpful replies.

 

[lookagain]

Determine whether or not each of the following arguments is valid.



2.)

Either I wear a red tie \(\displaystyle > > or < <\) I wear blue socks.
I am wearing blue socks.
-----------------------------------------------------------------------------------------------
I am not wearing a red tie

I have attempted to make a truth table to prove that it is valid, but I think I am missing a row. Any suggestions?

p q p \(\displaystyle > > or < <\)q ~p
T| T| T| F|
T| F| T| F|
F| T| T| T|
F| F| F| T|


Thanks for any helpful replies.

Regarding the two places of "or" here:

I take it to mean wear one or the other piece of clothing, but *not* both at the same time. (More restrictive)

For the "or" in the table (p V q), I take that to be p, q, as well as including both (also including p /\ q). (Less restrictive)