Definition
Mathematical logic
Mathematical logic studies statements and the rules for reaching valid conclusions.
What it means
Think of it as checking a chain of reasons. Start with facts or conditions, follow rules that keep each step valid, and decide what must be true—not merely what seems likely.
Remember it
Facts in, valid steps, conclusion out.
Example
Exactly one of two boxes holds a key. The red box is empty. Therefore the blue box holds the key. The conclusion is forced by the two given facts.
Watch for
Logic checks whether a conclusion follows from the assumptions. It does not guarantee that the assumptions themselves are true.
Common mix-up
A clever guess may be correct, but it is not a logical conclusion unless the reasons force it.
Exact meaning
In elementary mathematics, mathematical logic studies statements, their truth conditions, and rules of inference that determine when a conclusion follows from given assumptions.