Question

Give a formal proof of a valid argument. if not valid then give a counter example.
if Oscar attends class, then so does Miriam, and if Miriam attends class, so does George. Oscar attends class unless George attends. Therefore, Miriam does not attend class (O, M, G).

Answer 1

"Oscar attends class unless George attends".

This means "Oscar attends class only if George does not attend".

Formal Proof of a valid argument:

If O attends class, then so does M.

If M attends class, so does G.

Which implies "if O attends class, then so does G".

That is, only if O attends class, then George attends class.

Now, O attends class only if G does not attend. But from the above, only if O attends class, then G attends. Both these statements are contradictory. So, it leads to that both O and G does not attend class.

(It's because G follows O to the class but if G attends, then O does not attend and obviously, G does not attend).

Now, O does not attend class and so, M does not attend(since, M attends only if O attends).

Therefore, Miriam does not attend class.