Question

Let A and B be subsets of the universal set U. Prove that A\B⊆(U\B)\(U\A). Let A and B be subsets of the universal set U. Prove that A\B⊆(U\B)\(U\A).

Answer 1

To prove that A\B⊆(U\B)\(U\A), we need to show that every element in A\B is also in (U\B)\(U\A).

Step-by-step explanation:

To prove that A\B⊆(U\B)\(U\A), we need to show that every element in A\B is also in (U\B)\(U\A).

Let's consider an element x that belongs to A\B. By definition, x is in A and not in B. We want to prove that x also belongs to (U\B)\(U\A).

Since x is in A, it is in the universal set U. Since x is not in B, it is in the complement of B with respect to U, denoted as (U\B). Since x is not in A, it is not in the complement of A with respect to U, denoted as (U\A). Therefore, x is in (U\B)\(U\A).