If P, Q, R are Boolean variables, then (P + Q')(PQ' + PR)(P'R' + Q') simplifies

Simplify (P + Q')(PQ' + PR)(P'R' + Q')

1. Factor the middle term: PQ' + PR = P(Q' + R)

2. Substitute to get (P + Q') · P · (Q' + R) · (P'R' + Q')

3. Use absorption: P · (P + Q') = P, so expression becomes P · (Q' + R) · (P'R' + Q')

4. Distribute P over the sum: P · (P'R' + Q') = P·P'R' + P·Q' = 0 + PQ' = PQ'

5. Now multiply by (Q' + R): PQ' · (Q' + R) = PQ' (absorption) = PQ'

Final simplified form: PQ'