Question

If $P = \{1, 2, -1, 3\}$, $Q = \{0, 4, 1, 3\}$ and $R = \{1, 6, 7\}$, then $P \cap (Q \cup R)$ =

• A. $\{1, 2\}$
• B. $\{1, 3\}$
• C. $\{2, 1\}$
• D. $\{2, 3\}$

Hint:

When intersecting sets, always take the union first if required, then compare with the first set.

Answer 1

The Correct Option is B

Step 1: Compute $Q \cup R$.
$Q = \{0, 4, 1, 3\}$, $R = \{1, 6, 7\}$ Thus, $Q \cup R = \{0, 1, 3, 4, 6, 7\}$.
Step 2: Compute $P \cap (Q \cup R)$.
$P = \{1, 2, -1, 3\}$. Common elements with $Q \cup R$ are $\{1, 3\}$.
Step 3: Conclusion.
Thus, $P \cap (Q \cup R) = \{1, 3\}$.