Question

Let A U B = {a,b,c,d,e,x,y,z)andA n B = {b, e,y}. . a. If B - A = {x,Z}, then A=_________

Answer 1

A U B = {a, b, c, d, e, x, y, z}

A ∩ B = {b, e, y}

a. B - A is the complement of A in B; that is, from set B, we remove any elements found in A. Both sets contain b, e, and y, so if B - A = {x, z}, then

B = {b, e, x, y, z}

and so A makes up the rest of the given union,

A = {a, b, c, d, e, y}

b. A and B are non-empty, since their union and intersection are also non-empty. So if A - B = ∅, this means A contains all the elements of B, though B may have more elements than A. In other words, A is a subset of B, which means A U B = B. So

B = {a, b, c, d, e, x, y, z}

c. If B = {b, e, y, z}, then A makes up the rest of their union,

A = {a, b, c, d, e, x, y}

Then

A - B = {a, c, d, x}