1. The problem statement, all variables and given/known data So I was doing this problem in Munkres's Topology book: Determine whether the statement is true or false, If a double implication fails, determine whether one or the other of the possible implications holds: A ⊂ B or A ⊂ C ⇔ A ⊂ ( B ∪ C ) 2. Relevant equations - 3. The attempt at a solution I know that the ⇒ direction is true because (x∈A→x∈B or x∈A→x∈C)⇒(x∈A→(x∈B or x∈C)) For the other direction, I thought at first that it's true, but I checked some online answers and what I found is it's false. I thought it's true because what I had in mind is the word "or" stands for "either A is a subset of B, or A is a subset of C, or both". And if A is a subset of the union of B and C, then it's implied that A is a subset of at least one of them. What am I getting wrong? This is the answer that I found online: If the LHS statement is true then for each we have that and so , i.e. . The other direction is not correct though. Consider the sets then but it is not true that .