A variable $x$ is said to be live at a statement $S_i$ in a program if the following three conditions hold simultaneously: i. There exists a statement $S_j$ that uses $x$ ii. There is a path from $S_i$ to $S_j$ in the flow graph corresponding to the program iii. The path has no intervening assignment to $x$ including at $S_i$ and $S_j$ The variables which are live both at the statement in basic block 2 and at the statement in basic block 3 of the above control flow graph are

A variable $x$ is live at statement $S$ if there is an execution path starting from $S$ along which $x$ is used before being redefined.

Let us analyze the statements in basic blocks 2 and 3:

1. Basic Block 2 contains the statement v = r + u:

   • Variable $r$ is used in block 2 (and also in block 4: q = v + r), so $r$ is live at block 2.

   • Variable $u$ is used in block 2, so $u$ is live at block 2.

   • Variable $s$ is neither used in block 2 nor block 4, and is redefined in block 1 (s = p + q) before any use. Thus, $s$ is not live at block 2.

2. Basic Block 3 contains the statement q = s * u:

   • Variable $u$ is used in block 3, so $u$ is live at block 3.

   • Variable $s$ is used in block 3, so $s$ is live at block 3.

   • Variable $r$ is used downstream in block 4 (q = v + r), and there is no assignment to $r$ between block 3 and block 4. Thus, $r$ is live at block 3.

Taking the intersection of variables live at block 2 and block 3:

Hence, the variables live at both basic block 2 and basic block 3 are $r, u$, matching option C.