Exclusive disjunction operator
The exclusive disjunction
Previously we introduced the disjunction operator which is often represented in spoken English by the word “or”. An example of disjunction is the sentence “I like dogs or I like cats”. What does this really mean? The sentence has the meaning that I like dogs, or I like cats or, potentially, I like both dogs and cats. This type of “or” is called the inclusive disjunction because it is always an option that both of the propositions are true.
However, sometimes in spoken English there is a different type of “or”. Consider this: imagine being sat at a table and being asked if you would like cake or ice cream. In this situation, unless you are being cheeky, it probably isn’t expected that having both ice cream and cake is an option. What is meant in this situation is that you can have either cake or ice cream. This type of “or” is called the exclusive disjunction. Sometimes it is called the “exclusive or”.
The exclusive disjunction is represented by the (oplus) symbol, which is read as “exclusive or”. If (p) and (q) are propositions then the exclusive disjunction of (p) and (q) is the compound proposition that is true when exactly one of (p) and (q) are true and is false otherwise.
The truth table for the exclusive disjunction operator is provided below.
(p)
(q)
(p oplus q)
(F)
(F)
(F)
(F)
(T)
(T)
(T)
(F)
(T)
(T)
(T)
(F)
In the next step, we will look at the negation operator and how it differs from the previously introduced operations.
An Introduction to Logic for Computer Science
An Introduction to Logic for Computer Science
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