Disjunction operator
In the previous activity we looked at the conjunction operator. In this step, we will introduce the disjunction operator.
The disjunction operator
The statement “I like dogs or I like cats” is another example of a compound proposition as it is made up of two simpler propositions “I like dogs”, and the proposition “I like cats”. It appears to be similar to the conjunction we just learned about, however, it is different. Consider the two statements “I like dogs or I like cats” and “I like dogs and I like cats”. What is the difference? Can you describe the difference in spoken English, perhaps to a friend?
The statement “I like dogs or I like cats” is an example of a disjunctive proposition. The word “or” in the compound proposition has a special purpose. It conveys the concept of disjunction. Consider the statement carefully; when is the statement true? Consider your friend saying it to you.
The statement is true in three circumstances:
- When your friend likes dogs, or
- When your friend likes cats, or
- When your friend likes both cats and dogs.
Now, think about when the compound proposition is false. If your friend said “I like dogs or I like cats” to you, and you knew they were not telling the truth, then you would know that your friend does not like dogs and they do not like cats.
In logic we have a symbol that represents the disjunction operator. Let
(p) represent the proposition “I like dogs” and let (q) represent the proposition “I like cats”. The compound proposition “I like dogs or I like cats” can be represented as (p lor q), which is read as “p or q”.
We can describe a disjunctive compound proposition using the truth table below. Check if your understanding of disjunction is correct by reasoning about the meaning of the compound proposition “I like dogs or I like cats” when the proposition “I like dogs”, and the proposition “I like cats” are true or false. The table summaries what the correct reasoning is.
| (p) | (q) | (p lor q) |
| (F) | (F) | (F) |
| (F) | (T) | (T) |
| (T) | (F) | (T) |
| (T) | (T) | (T) |
In the next step, we will look at the exclusive disjunction 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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