The discussion centers on proving the mathematical statement that the difference between sets A and B, denoted as A \ B, is empty (∅) if and only if A is a subset of B (A ⊆ B). The participants clarify that if A is a subset of B, then removing all elements of A from B results in an empty set. The mathematical expression can be formally written as: "For all x in A, x is in B," which establishes the necessary proof.
PREREQUISITESStudents studying set theory, mathematics educators, and anyone interested in formal mathematical proof techniques.
Kaldanis said:Homework Statement
Let A and B be sets.
Show that A \ B = ∅ if and only if A ⊆ B.I think this means that A is a subset of B, therefor if I remove all the elements of A that are in B, A would end up being empty (or ∅).
How do I write this mathmatically or is the above sentence acceptable?