The compound statement P v Q is only true when P is true or Q is true.
P = The Man is running
Q = The Man is walking
P OR Q
The man is walking OR the man is running.
Although the Man cannot run and walk at the same, the truth table shows that if the Man could run and walk at the same time then P OR Q would be be true.
P= The Car Engine is running
Q=The Car Radio is on
Now the truth table seems to make more sense because we can experience both these things can happen at the same time.
So, the Car Engine is running OR the Car Radio is on, makes sense even if both things were happening at the same time (simply because they can happen at the same time).
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OR is associative so it can be used without any ambiguity.
((P v Q) v R) <=> P v Q v R