This is where the mistake is. If you flip the brown card and the number is even, you have disproved the proposition that even cards have red backs. If you flip the brown card and the number is odd, you have proved nothing. There is no proposition about brown or odd cards being tested. The only proposition being tested is that red cards have even numbers, In your words, "there is no rule that states that odd cards cannot be red". Equally, there is no rule that states that an odd card MUST have a different color than an even card. Only in the case that odd cards MUST have different colors than even cards will revealing a brown card with an odd number give you any information about even cards or red colors. That case does not exist in the directions given. The reader might infer that this is an "exclusive or " proposition, as stated in logic, "if a then not b, if b then not a". The author has not constructed the test as an exclusive or proposition. Read the descriptions again, you will find neither declaration nor implication that odd and even numbered cards MUST have different colors on their backs, just as you will find no declaration or implication that brown and red cards MUST have numbers with different odd/even status. Unless the directions state these postulates then they can not be assumed, and the status of a brown card or an odd numbered card cannot be presumed to have any relationship to that of red cards and even numbered cards.

This is a different test than the drinking test, where the proposition being tested is the legality of the drink in front of the drinker. Since nowhere in the North American continent is it legal for a 16 year old to drink alcoholic beverages it might be safely assumed that this is a condition of the test, that an alcoholic drink in front of a 16 year old is a breach of law. There is no similar rule implied or stated in the case of the cards. As to the truth table, to put it indelicately, GIGO:)