Question

question 13 use the following venn diagram to find ( a setminus u ). venn diagram: universal set ( u ) (rectangle) contains circle ( a ) (purple, elements: ( a, b, c, d, e )) and circle ( b ) (green, elements: ( d, e, f, g, h, i )); elements ( j, k, l, m ) are in ( u ) outside both circles. options: ( {b, g, s, u, y} ), ( {c, e, m, x, z} ), ( {f, j, q, t, x} ), ( {d, i, s, t, v} ), ( {d, e, h, m, z} ), ( emptyset )

Explanation:

Step1: Recall Set Difference Definition

The set difference \( A \setminus U \) (read as "A minus U") is the set of elements that are in \( A \) but not in \( U \). By definition of the universal set \( U \), every element of \( A \) is also an element of \( U \) (since \( U \) contains all elements under consideration, including those in \( A \) and \( B \)).

Step2: Determine Elements in \( A \setminus U \)

Since all elements of \( A \) are within \( U \) (as \( U \) is the universal set containing \( A \) and \( B \) and the surrounding region), there are no elements in \( A \) that are not in \( U \). So the set \( A \setminus U \) is the empty set.

Answer:

\(\emptyset\)