Mathematical logic problem

Question

Could somebody please help me solve the following logic-problem (it's translated, so I hope it makes sense):

Facts:

1. If Michael coughs and his face is white, he is either sick or has gone around the corner to smoke
2. If Michael hasn't smoked and still has a cough or is white in the face, then he is sick.
3. When Michael is sick, he coughs, but his face is not white.

When Michael came to class after the break, his face was completely white. What is the conclusion - is he sick or did he have a smoke break?

Thanks!

Answer 1

Assume the following hold:

$(1)\text{ }$ $(A\wedge B)\implies (C\vee D)$,

$(2) \text{ }$ $(\neg D\wedge (A\vee B))\implies C$,

$(3)\text{ }$ $C\implies (A\wedge \neg B)$

Then the question asks which of the following also holds?: $$B\implies C\text{ }\text{ }\text{ or }\text{ }\text{ }B\implies D$$ Make a truth table for all statements involved and find rows where all of (1-3) are true, if a conclusion is true in the same rows as these are true then logical implication has been found.