The sets P and Q consists of the points whose coordinates (x, y) are given by P = {(x, y) : y = 2x + 3} and Q = {(0, 0), (0, 3), (1, 5), (2, 5), (3, 9)} respectively.

1. Identify the meaning of $P \cap Q$ and test elements of $Q$ against the rule for $P$.

$P$ contains all points satisfying $y=2x+3$.

For each point in $Q$:

$(0,0):\quad 0 \ne 2(0)+3=3$, so $(0,0) \notin P$.

$(0,3):\quad 3=2(0)+3$, so $(0,3) \in P$.

$(1,5):\quad 5=2(1)+3$, so $(1,5) \in P$.

$(2,5):\quad 5 \ne 2(2)+3=7$, so $(2,5) \notin P$.

$(3,9):\quad 9=2(3)+3$, so $(3,9) \in P$.

2. List the elements common to $P$ and $Q$.

The elements of $Q$ that also belong to $P$ are

$(0,3),\ (1,5),\ (3,9).$

Therefore,

$P \cap Q=\{(0,3),(1,5),(3,9)\}.$

1. Simplify the set expression to identify the required Venn diagram region.

$(P' \cup Q)' = (P')' \cap Q' = P \cap Q'$
So the required region is the part of $P$ that is not in $Q$.