To find the set \((P - Q) \cap R\), we first need to find the difference between sets \(P\) and \(Q\) (i.e., \(P - Q\)) and then find the intersection of the result with set \(R\).

The set difference P - Q consists of elements that are in set P but not in set Q.

Given:

P = {1, 2, u, v, w, x}

Q = {2, 3, u, v, w, 5, 6, y}

So, P - Q will contain elements from P that are not in Q:

P - Q = {1, x}

Now, we need to find the intersection of (P - Q) with set (R):

(R = {2, 3, 4, v, x, y}

\((P - Q) \cap R\) will contain elements that are common to both sets (P - Q) and (R):

\((P - Q) \cap R = \{x\}\)