Question

Which law is used to come to the stated conclusion? If no conclusion can be drawn, answer "no conclusion". If Rae is the driver today then Maria is the driver tomorrow. Annis the driver today.

Answer 1

DEFINITIONS:

1) Law of Contrapositive: This law reverses the conclusion and the hypothesis of the inverse of the conditional statement. This is expressed as:

`\begin{gathered} \text{Original Statement: If p, then q} \\ \text{Contrapositive Statement: If not q, then not p} \end{gathered}`

2) Law of Detachment: This law states that if the conditional statement is true, and the hypothesis is true, then the conclusion is true as well. This is expressed as:

`\begin{gathered} 1)\text{ If p, then q} \\ 2)\text{ p} \\ \text{Then},\text{ statement q is true} \end{gathered}`

3) Law of Syllogism: This law is explained as:

`\begin{gathered} 1)\text{ If p, then q} \\ 2)\text{ If q, then r} \\ \text{Then,} \\ 3)\text{ If p, then r is true} \end{gathered}`

QUESTION:

The statements provided can be separated as shown below:

`\begin{gathered} 1)\text{ p = Ray is the driver today} \\ 2)\text{ q = Maria is the driver tomorrow} \\ 3)\text{ r = Ann is the driver today} \end{gathered}`

The question states that

`\text{If p, then q}`

and

`r\text{ is true}`

This conclusion cannot be proved using any of the rules above.

Therefore, no conclusion can be drawn on the truth of the statement.