Here is the completed truth table:
P | q | R | (q v r) | P1 | P1^(q v r)
--|---|---|--------|----|-----------
T | T | T | T | F | F
T | T | F | T | F | F
T | F | T | T | F | F
T | F | F | F | F | F
F | T | T | T | T | T
F | T | F | T | T | T
F | F | T | T | T | T
F | F | F | F | T | T
In this table, P, q, and R are boolean variables that can take on the values of either T (true) or F (false).
The column labeled "(q v r)" represents the logical OR operation between q and R, where "v" represents the OR operator. The result of the OR operation is true (T) if either q or R (or both) is true, and false (F) otherwise.
The column labeled "P1" represents a second boolean variable that is independent of P, q, and R.
The column labeled "P1^(q v r)" represents the logical AND operation between P1 and (q v r), where "^" represents the AND operator. The result of the AND operation is true (T) if both P1 and (q v r) are true, and false (F) otherwise.