Understanding the Logical Operator Disjunction (∨) and its Truth Values | A Guide

p ∨ q

In mathematical logic, the symbol “∨” represents the logical operator called “disjunction

In mathematical logic, the symbol “∨” represents the logical operator called “disjunction.” The expression “p ∨ q” is a logical statement that is read as “p or q.”

In simple terms, “p ∨ q” means that either p is true, or q is true, or both can be true. The disjunction “∨” is inclusive, which means that if either p or q is true, then the entire expression “p ∨ q” is true.

Here is a truth table demonstrating the possible combinations of truth values for p and q, as well as the resulting truth values for “p ∨ q”:

| p | q | p ∨ q |
| — | — | —– |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |

As you can see, in the truth table, “p ∨ q” is true whenever at least one of p or q is true. It is only false when both p and q are false.

Let’s illustrate this with an example:

Suppose p represents the statement “It is raining,” and q represents “The sun is shining.”

Then, “p ∨ q” translates to “It is raining or the sun is shining.” The statement “p ∨ q” would be true if it is either raining or the sun is shining. It would only be false if neither statement is true, meaning it is not raining and the sun is not shining.

I hope this explanation helps! If you have any further questions or need clarification, feel free to ask.

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