Question

If $A=\{1,2,3,4,5\}$ and $B=\{2,4,6\}$, then $A-B=$

• A. {1,3,5,6}
• B. {0,1,3,5,6}
• C. {1,3,5}
• D. {1,2,3,4,5,6}
• E. {2,4}

Hint:

Set Theory Tip: When calculating $A - B$, completely ignore any elements in B that aren't in A (like the number 6). Only focus on what needs to be removed from A.

Answer 1

The Correct Option is C

Concept:
The set difference $A - B$ consists of elements that are in set A but not in set B. $$A - B = \{x \mid x \in A \text{ and } x \notin B\}$$

Step 1: Identify elements of set A.
Write down all elements present in the first set: $$A = \{1, 2, 3, 4, 5\}$$

Step 2: Identify elements of set B.
Write down all elements present in the second set: $$B = \{2, 4, 6\}$$

Step 3: Find the intersection (common elements).
Compare both sets to find which elements appear in both A and B: $$A \cap B = \{2, 4\}$$

Step 4: Perform the set subtraction.
Take set A and remove the common elements found in
Step 3: $$A - B = \{1, 2, 3, 4, 5\} - \{2, 4\}$$

Step 5: Determine the final set.
After removing 2 and 4, the remaining elements from set A form the final answer: $$A - B = \{1, 3, 5\}$$ Hence the correct answer is (C) {1,3,5\.