Hi This is a question from my self study of ch.2 of Alfred Tarski's Introduction to Logic Which of the following implications are true from the perspective of mathematical logic? a) If a number x (assuming x is an integer) is divisible by 2 or by 6, then it is divisible by 12 b) if 18 is divisible by 3 and by 4, then 18 is divisible by 6 Both statements are obviously false from the standpoint of ordinary language. However, as far as my reasoning for b) goes, it is a logically true statement, because the antecedent (18 divisible by 3 and 4) is false, thus the truth table values of the statement will be either FF or FT, leading to overall true meaning of the statement. I find a) to be more confusing. It is clearly untrue (18 and 6 are counterexamples) yet looking at the antecedent and consequent separately, can lead me to believe that the statement can be true from a logical perspective. For instance if it's true that X is divisible by 2 or 6, but false that it is divisible by 12, then the statement is false. On the other hand, if x is divisible by 12 then the statement is true. Am I mired in confusion here? My question is, am I correct in trying to view this kind of problem in terms of truth tables? Sometimes the truth value of the antecedent and consequent can be confusing or ambiguous, even though the overall meaning of the statement may appear obvious.