Inclusive disjunction facts for kids

A Venn diagram showing "A or B"

A Venn diagram showing "A or B or C"

Inclusive disjunction, often just called or, is a basic idea in logic. It helps us combine two statements to make a new one. This new statement is true if at least one of the original statements is true.

Think of it like this: If you say, "I will eat pizza or I will eat pasta," this statement is true if you eat pizza, or if you eat pasta, or if you eat both! The only way it's false is if you eat neither pizza nor pasta.

In logic, we use a special symbol for "or": . So, if we have two ideas, let's call them A and B, then "A B" means "A is true, or B is true, or both A and B are true."

This is different from something called exclusive disjunction. Exclusive disjunction means "either A or B, but not both." For example, "You can have cake or ice cream for dessert" usually means you pick one, not both. Inclusive disjunction, however, allows for both.

How "Or" Works

The "or" operation takes two "truth values" as input. A truth value is simply whether a statement is true or false. It then gives one truth value as an output.

Here's a simple way to see it:

• If the first statement is true, and the second statement is true, then "or" is true.
• If the first statement is true, and the second statement is false, then "or" is true.
• If the first statement is false, and the second statement is true, then "or" is true.
• If the first statement is false, and the second statement is false, then "or" is false.

The only time "or" is false is when both parts are false.

Everyday Examples

We use inclusive disjunction all the time without even realizing it.

• "You need a pen or a pencil to write." If you have either one, or both, you can write.
• "The store is open on Saturday or Sunday." This means it's open on at least one of those days, possibly both.

Related Ideas

• Alternative: Another word for a choice or option.
• Boolean algebra: A type of math that uses true/false values and operations like "and," "or," and "not."
• Logical conjunction: This is the "and" operation. It's only true if both parts are true.
• XOR gate: This is a type of electronic circuit that performs the exclusive "or" operation.

Images for kids

• 

  A friendly robot