(Set Operations and Relations LC)Given A = {1, 2, 5, 7} and B = {1, 3, 5, 7, 8}, find B – A. {2} {3, 8} {1, 5, 7} {1, 2, 3, 5, 7, 8}

1. Break Down the Problem

We need to find the set difference $B - A$, which means we will identify the elements that are in set $B$ but not in set $A$.

2. Relevant Concepts

The set difference $B - A$ is defined as: $B - A = \{ x \in B \mid x \notin A \}$

3. Analysis and Detail

1. Identify the elements of sets $A$ and $B$:

   • $A = \{1, 2, 5, 7\}$
   • $B = \{1, 3, 5, 7, 8\}$

2. Find elements in $B$ that are not in $A$:

   • Check each element of $B$:
     • $1$: in $A$, skip
     • $3$: not in $A$, include
     • $5$: in $A$, skip
     • $7$: in $A$, skip
     • $8$: not in $A$, include

Thus, the elements of $B$ that are not in $A$ are $\{3, 8\}$.

4. Verify and Summarize

We have identified and confirmed that the elements in $B$ (3 and 8) are not in $A$. No further elements from $B$ need to be checked.

Final Answer

$B - A = \{3, 8\}$