Final answer:
No, the truth value of a bi-conditional cannot be determined by knowing only the truth value of its left-hand side, as both sides must be known to determine the truth of the bi-conditional.
Step-by-step explanation:
No, one cannot know the truth value of a bi-conditional if one only knows the truth value of its left-hand side. Bi-conditional statements operate such that the truth values of both sides must either both be true or both be false for the entire statement to be true. Knowing only one side does not provide sufficient information about the other.
For instance, the bi-conditional statement 'if and only if P then Q' (P ↔ Q) is true if both P and Q are true, or both are false. So, if you know that P is true, you cannot determine the truth of Q without additional information. Similarly, if P is false, knowing whether Q is true or false would still be necessary to establish the truth of the bi-conditional statement.
Using the example mentioned earlier, 'if you are a bachelor, then you are unmarried' (B ↔ U), if we only know someone is a bachelor (B is true), we can deduce that the person is unmarried (U is true) with a conditional, but not with a bi-conditional without the reverse being explicitly known.