Question

use the following venn diagram to find ( a setminus b ).
venn diagram: two circles a (purple) and b (green) in a universal set. a’s non - overlapping region has a, b, c; overlapping region with b has d, e. b’s non - overlapping region has f, g, h, i; universal set outside both has j, k, l, m. options: {c, l, p}, {a, e, p}, {j, m, w}, {a, m, u}, {a, b, c}, ( emptyset )

Explanation:

Step1: Recall the definition of set difference

The set difference \( A \setminus B \) (read as "A minus B") consists of all elements that are in set \( A \) but not in set \( B \).

Step2: Identify elements in set \( A \)

From the Venn diagram, set \( A \) (the purple circle) contains elements \( a \), \( b \), \( c \), \( d \), \( e \).

Step3: Identify elements in set \( B \)

Set \( B \) (the green circle) contains elements \( d \), \( e \), \( f \), \( g \), \( h \), \( i \).

Step4: Find elements in \( A \) but not in \( B \)

We need to remove the elements of \( B \) from \( A \). The elements common to both \( A \) and \( B \) are \( d \) and \( e \). So, the elements in \( A \) but not in \( B \) are \( a \), \( b \), \( c \).

Answer:

\(\{a, b, c\}\)