#Discrete

Question

Answer 1

This seems a standard problem. Simply Check if the given argument is valid or not.If invalid then give a counter-example on which the argument is fails. 

7  $\underbrace {[(z \cup y) \cap (y \rightarrow x) \cap \neg x] }\rightarrow \underbrace{ \neg z}$ 
                           $ T $                                 $F$

Try to make RHS $false$ and LHS $true$. We can easily see that for $z=T, y=F,x=F$ the argument fails.

Option (E) is correct.

Similarly 8 will fail on $w=F, x=F,y=F,z=T$, Option (A)

9 will fail on Option (A) and 10 will fail on Option (B). 

None of the given arguments is valid.