Understanding Logical Disjunction | The Symbol ∨ and its Truth Table

p∨q (disjunction of p and q)

The symbol “∨” represents a logical operation called “disjunction

The symbol “∨” represents a logical operation called “disjunction.” When we have two propositions, p and q, the disjunction of p and q (p∨q) is a compound proposition that is true if at least one of the individual propositions, p or q, is true. In other words, the disjunction is false only if both p and q are false.

Here is a truth table representing the possible combinations of truth values for p and q, along with the resulting truth value of p∨q:

| p | q | p∨q |
|:—–:|:—–:|:—–:|
| false | false | false |
| false | true | true |
| true | false | true |
| true | true | true |

As you can see, p∨q is true in all cases except when both p and q are false.

For example, let’s say p represents the statement “It is raining” and q represents the statement “It is sunny.” The disjunction p∨q would be true if it is either raining or sunny, but false if it is neither raining nor sunny.

So, in general, the disjunction p∨q is true when at least one of the propositions p or q is true.

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