Determine if the following argument is valid or invalid?

Question

Determine if the following argument is valid or invalid by comparing their symbolic forms with other known forms or constructing a truth table.

The sun is shining and the sky is clear.
The sky is not clear or the sun is shining.
Therefore, the sun is not shining.

A. valid
B. invalid

Answer 1

Let s,c be two boolean variables

s-the sun is shining
c-the sky is cleat

The sun is shining and the sky is clear.
s * c

The sky is not clear or the sun is shining:
!c + s

If s=1 then s*c =c, so we need c to be 1 in order for the sun to shine.

In this case, !c + s = 0+s = s

s=c=1 satisfies both arguments.

The abswer is B.

Answer 2

"If I hear that poem, then i'm reminded of my mom. If i'm getting sentimental, then i'm no longer reminded of my mom." this fact would properly be simplified to P --> Q R --> ~Q the place P is "I hear the poem", Q is "i'm reminded of my mom", and R is "i'm getting sentimental" The question is not any count if this fact is valid of no longer "i'm getting sentimental. for this reason, i do no longer hear the poem." that's simplified to: R --> ~P utilising those statements, we can deduce that R --> ~P is is valid or no longer P --> Q R --> ~Q utilising regulation a million, if R is genuine and R --> ~Q, then ~Q is genuine utilising regulation 2, if ~Q is genuine and P --> Q, then ~P is genuine for this reason if R is genuine, then ~P is valid (R --> ~P) for this reason, this would properly be a valid fact.