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Logic Worksheets

Click on the Logic worksheet set you wish to view below.

  1. Completing Truth Tables
  2. Conditionals [asks for Logic Table]
  3. Conjunctions [asks for Logic Table]
  4. Disjunctions Using Logic Tables
  5. Function Table Worksheet Maker

Who invented logic?

Mathematical (symbolic) logic developed in the 1800s. George Boole, and English mathematician and philosopher developed it as a tool to investigate fundamental principles in mathematics. His contribution was so important that his name is used to identify a branch of mathematics based on logic and symbols - Boolean Algebra.

What does logic mean in mathematics?

Sometimes called formal logic, in mathematics logic uses strict rules to draw conclusions. Proofs in mathematics are based on these formal rules and procedures. The reason for this is that we want to discover mathematical truths and eliminate doubt.

Compare this to the sort of arguments people normally make - they are based on a standard like the one used in courts, beyond a reasonable doubt. The mathematical standard is much higher, the rules are much stricter but the results are considered valid and beyond question.

Logic also gives us the tools to generalize. We can say with certainty that a property of one number (or a relationship between numbers) will apply to all numbers without having to check every single case.

How is formal logic used?

When problems are stated in natural language, they are usually open to interpretation. By recasting the information in the language of formal logic, they are less ambiguous. The problem and its solution are clear.

If we say, "At the mall, you can get clothes or CDs" we mean you can get either of those things or both of those things. But if we say, "Mary bought CDs or clothes today" we mean she bought one or the other, but not both. The rules of logic clear this up with the idea of an inclusive or (could be both, but is at least one) and an exclusive or (one or the other, but not both).

In this way, logic turns common sense into a more precise form that can be handled with the other tools of mathematics. This is especially important for mathematical proofs.

A basic problem in logic.

Proving there is no largest number might look like this in logic:

Natural Language
Mathematical Statement
Comments
Suppose there is some number larger than all other numbers
∃!x: x > N
There exists some x such that x is greater than any other number.
You can add one to any number and get a bigger number.
(x + 1) > x
If you add one to x, you get a quantity greater than x.
No number can be largest, because you can always add one to it and get a larger number.
~∃x : x > x + 1
There does not exist any x such that x is greater than x plus one.
Our first statement must be wrong and there isn't any largest number.
∃!x: x > N = F

∴ ~∃ x : x > N = T
The proposition that there is a greatest number is false, so the opposite must be true.

 

An interesting fact about logic.

Although Boolean algebra was invented in the 19th century, it has proven indispensable in computer programming. Because computers need clear rules and don't understand natural language, symbolic logic has become one of the most important topics for computer scientists to learn.

The normal true or false answer from logic is an ideal fit with the on/off, yes/no character of computers. Every time you press a key or move your mouse, you are asking the computer to solve a problem in mathematical logic!


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