Final answer:
When the left-hand conjunct of a conjunction is false, the truth value of the conjunction depends on the truth value of its right-hand side.
Step-by-step explanation:
Conjunction and Truth Value
When the left-hand conjunct (the left side of the dot symbol) of a conjunction is false, the truth value of the conjunction as a whole is determined by the truth value of its right-hand side. This is because in a conjunction, both the left and right conjuncts must be true for the conjunction to be true.
If the left conjunct is false, regardless of the truth value of the right conjunct, the conjunction will be false.
For example, let's say we have the conjunction 'A and B'. If A is false and B is true, the conjunction as a whole is false.
However, if A is true and B is false, the conjunction will still be false because both conjuncts must be true for the conjunction to be true.