Question
P ↔ (Q v R)

Answer

Fact sheet:
Column $\rightarrow$ 1 2 3 4 5
Row $\downarrow$ P Q R Q v R P $\leftrightarrow$ (Q v R)
1 T T T T T
2 T T F T T
3 T F T T T
4 T F F F F
5 F T T T F
6 F T F T F
7 F F T T F
8 F F F F T
        2, 3 (v) 1, 4($\leftrightarrow$)
Explanation: P ↔ (Q v R) is the column no. 1, 2 and 3 are the pillars, while
The remaining two are secondary columns. Column no. 5 presents the whole complex joint statement. Column no. Looking at 5, the following facts become clear:
(1) According to the first row, if P is truth, Q is truth and R is truth, then P ↔ (Q v R) is the whole statement truth.
(2) According to the second row, if P is true, Q is true and R is false, then P P (Q v R) is the whole statement truth.
(3) According to the third row, if P is true, Q is untrue and R is true, then P ↔ (Q v R) is the whole statement truth.
(4) According to the fourth row, if P is true, Q is untrue and R is untrue, then P ↔ (Q v R) is the whole statement untrue.
(5) According to the fifth row, if P is untrue, Q is true and R is true, then P ↔ (Q v R) is the whole statement untrue.
(6) According to the sixth row, if P is untrue, Q is true and R is untrue, then the whole statement P ↔ (Q v R) is untrue.
(7) According to the seventh row, if P is untrue, Q is untrue and R is true, then P ↔ (Q v R) is the whole statement untrue.
(8) According to the eighth row, if P is untrue, Q is untrue and R is untrue, then the whole statement P ↔ (Q v R) is true.

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