Show whether this statement is true or false. Let S be a nonempty set and let T be a collection of subsets of?

S. If AnB=nonempty set for all pairs of A, B or elements of T, then there exists an element x is an element in S such that x is an element in c for all c is an element is T.





My answer is false because if you let s={1,2,3} then x = 1 and c = {1} where T = {{1}} which shows how then T is not a subset of S





Is this corrrect??Show whether this statement is true or false. Let S be a nonempty set and let T be a collection of subsets of?
The answer is ';false';. However, your reasoning doesn't make any sense. T isn't supposed to be a subset of S - its elements are subsets of S.





Try using that same set for S = {1, 2, 3}, but instead of starting with x (which we want to claim doesn't exist), try understanding the actual statement and creating a collection of subsets for T.