Final answer:
The truth value of a conjunction is false if its left-hand conjunct is false, because both parts of a conjunction need to be true for the entire statement to be true.
Step-by-step explanation:
If the left-hand conjunct of a conjunction is false, the truth value of the entire conjunction is false as well. In logical conjunction, both conjuncts must be true for the whole statement to be true.
In the context of logical reasoning, a conjunction is a compound statement formed by connecting two statements with the word 'and'. This compound structure only yields a true outcome when both the left-hand and right-hand conjuncts are true. So, when we encounter a false statement on the left side of a conjunction (as represented by the 'dot' symbol in formal logic, often read as 'and'), we have enough information to determine that the compound statement cannot be true, irrespective of the truth value of the right-hand conjunct. Think of it as a strict requirement: both conditions must be met, or the deal's off.
As an example, consider the statement 'The sky is blue and pigs can fly'. If it is known that 'pigs can fly' is false, it does not matter whether the sky is blue; the whole statement is considered false because not both parts are true.