Question

How would I create a logic proof for this question?

Answer 1

Let us represent the premises given:

$\begin{gathered} \text{Let } \\ A=\text{John is aardvark} \\ C=\text{Charles has a blue eye} \\ B=\text{Bob counts} \\ E=\text{Edna drives a truck} \\ D=\text{Dan edits} \end{gathered}$

Then

We can subdivide the argument into substatement

Statement 1: If John is an aardvark then either Charlene has blue eyes or Bob counts

$A\Rightarrow(C\lor B)$

Statement 2: If Charlene has a blue eye then Edna drives a truck

$C\Rightarrow E$

Statement 3: Either John is an aadvark or Dan edits

$A\lor D$

Statement 4: Moly claims that either Bob counts or Edna drives a truck, but Moly is wrong

$\begin{gathered} (B\lor E),\text{ But} \\ \sim(B\lor E) \end{gathered}$

Therefor D

$\therefore D$

The above hypothesis and conclusion can be summarized below as;

Using a truth table calculator, the validity of the above arguments is shown below

Hence, we can conclude that the above is a valid argument.