Let \(𝑃−𝑖\) and \(𝑃_𝑗\) two processes, R be the set of variables read from…

Correct answer: The condition R(P_i) ∩ R(P_j) = Φ is not required for safe concurrent execution.

Required conditions for conflict-free concurrent execution:

• R(P_i) ∩ W(P_j) = Φ — no read–write overlap from the first process reading what the second writes.

• W(P_i) ∩ R(P_j) = Φ — no write–read overlap from the first process writing what the second reads.

• W(P_i) ∩ W(P_j) = Φ — no write–write overlap, as concurrent writes to the same variable cause conflicts.

Explanation:

Two processes may read the same memory location at the same time without causing a data race or inconsistency, so the intersection of their read sets can be non-empty. In contrast, any overlap between reads and writes (in either direction) or between writes and writes can produce race conditions or inconsistent updates, so those intersections must be empty for safe concurrent execution.