Exclusive disjunction facts for kids
Exclusive disjunction (also known as exclusive or or XOR) is a special kind of logic rule that works with two different ideas or statements. It's often shown using symbols like 
or 
.
Think of XOR like this: it's true if exactly one of the two ideas is true, but not both. If both ideas are true, or if both are false, then XOR says the result is false. This means XOR is true only when the two ideas are different from each other. If they are the same, the result is false.
A simple way to remember XOR is: "One or the other, but not both!"
This makes XOR different from inclusive disjunction (which is usually just called "OR"). Regular "OR" is true if one, or the other, or *both* ideas are true. XOR is more picky!
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| Venn diagram showing XOR for two sets, A and B. |
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| Venn diagram showing XOR for three sets, A, B, and C. |
Contents
What is a Truth Table?
A truth table is a helpful chart that shows all the possible outcomes for a logic rule like XOR. It lists every combination of "true" (T) and "false" (F) for the ideas involved and then shows what the final result will be.
How XOR Works: The Truth Table
Let's look at the truth table for 
. Here, 'p' and 'q' stand for our two different ideas or statements.
| p | q | ⊕ |
|---|---|---|
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
- If 'p' is false and 'q' is false, then XOR is false. (They are the same.)
- If 'p' is false and 'q' is true, then XOR is true. (They are different.)
- If 'p' is true and 'q' is false, then XOR is true. (They are different.)
- If 'p' is true and 'q' is true, then XOR is false. (They are the same.)
You can see that the result of XOR is only true when 'p' and 'q' have different truth values.
Where is XOR Used?
XOR is very important in computer science and digital electronics. Computers use XOR for many tasks, like:
- Checking for differences: If you want to know if two things are exactly the same or different, XOR can tell you.
- Error detection: Sometimes, data can get corrupted. XOR can be used to create special codes that help detect if there's an error in the data.
- Cryptography: XOR is also used in some simple ways to encrypt (or scramble) information, making it harder for others to read without the right key.
Related pages
See also
In Spanish: Disyunción exclusiva para niños
