Disjunction
The disjunction is a logical connective that establishes an “or” relationship between two statements. It is commonly symbolized using the “∨” symbol.
a ∨ b
The statements that make up a disjunction are called “disjuncts”.
If either disjunct is true, then the overall disjunction is true. If, however, both disjuncts are false, then the overall disjunction is false.
Furthermore, the disjunction establishes an “inclusive-or” relationship, meaning, if one disjunct is true, it does not necessarily mean the other disjunct is false; both disjuncts can potentially be true.
That said, given a disjunction, we can only safely conclude that at least one disjunct is true.
Let us solidify our understanding using a quick example: “Either the dog barks (B) or the cat runs away (R)”.
B ∨ R
Given this disjunction, can we say that the statement B is true? Can we say that R is true? Can we say that both B and R are true?
While it is possible that all three scenarios are true, we cannot say with certainty that either B is true, R is true, or that both B and R is true: We can only infer that at least one of the statements, B or R, is true.
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app now:
The disjunction is a logical connective that establishes an “or” relationship between two statements. It is commonly symbolized using the “∨” symbol.
a ∨ b
The statements that make up a disjunction are called “disjuncts”.
If either disjunct is true, then the overall disjunction is true. If, however, both disjuncts are false, then the overall disjunction is false.
Furthermore, the disjunction establishes an “inclusive-or” relationship, meaning, if one disjunct is true, it does not necessarily mean the other disjunct is false; both disjuncts can potentially be true.
That said, given a disjunction, we can only safely conclude that at least one disjunct is true.
Let us solidify our understanding using a quick example: “Either the dog barks (B) or the cat runs away (R)”.
B ∨ R
Given this disjunction, can we say that the statement B is true? Can we say that R is true? Can we say that both B and R are true?
While it is possible that all three scenarios are true, we cannot say with certainty that either B is true, R is true, or that both B and R is true: We can only infer that at least one of the statements, B or R, is true.
Want an interactive way to learn logic?
Enhance your critical thinking skills with Symbols Logic. Unlock access to the first studycard and the first level of all activities for free. Get the app now: