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Can a conjecture be used to explain the steps of a proof?
No. A conjecture itself has not been proved true (nor false), but is believed, on the evidence so far, to be true. If it is at some stage in the future actually proved to be false any proof based on it would immediately be useless as anything can be proved to be true from a false premise, and this includes false statements. For example consider a father who always tells his child the truth and consider the statement a father gives his son: "If you are not in bed by 8pm then I will not read you a story". If the child in not in bed by 8pm, then the father will not read them a story. ie if the premise of not being in bed by 8pm is true, it is proved that no story is read. However, if the child is in bed by 8pm, the premise of not being in bed by 8pm is false (ie the child is in bed by 8pm) nothing can be inferred about a story being read: the father may read a story, or he may not read a story. The conjecture concerns the time the child is in bed: If the child is in bed by 8pm, and the father does read a story, the father made a true statement. If the child is in bed by 8pm, and the father does not read a story, the father still made a true statement! This may seem illogical (and cruel), but the father has only said what will happen if the child is not in bed by 8pm; he has said nothing about what will happen if the child is in bed by 8pm. It is very logical and is the "implies" (→) logic table: T → T = T T → F = F F → T = T F → F = T If the first statement is true, the result is the truth of the second statement. If the first statement is false, the result is true regardless of the truth of the second statement. So if a conjecture is the first statement, only if it is [proved true] true does it say anything about the truth of the following statement.
Is it true that in an answer that has four significant figures two are estimated and two are known?
False, one is estimated and three are known
My father asked me abruptly, "You'd rather write than preach, wouldn't you" Why does this conversation surprise the narrator?
The only moment of true connection he had with his father (Apex)
True or false A person known to embellish is not a plain speaker?
False
Is it true or false that if you create logical subdirectories you can more easily locate individual files?
true
