The Truth of Sentences with Coordinating Conjunctions

We can make sentences with the coordinating conjunctions "and", "or" and "but" to determine the relationship between the independent clauses of each sentence and ultimately the entire sentence. An exercise which illlustrates this gives a value of 0 to a clause and sentence which is false and a value of 1 to a clause and sentence which is true.

Let us start with the conjunction "and". Consider the following sentences:

Celine Dion is Canadian and Faith Hill is American. {1,1} = 1
Celine Dion is Canadian and Faith Hill isn't American. {1,0} = 0
Celine Dion isn't Canadian and Faith Hill is American. {0,1} = 0
Celine Dion isn't Canadian and Faith Hill isn't American. {0,0} = 0

With the conjunction "and", we see that both independent clauses must be true for the entire sentence to be true. Now let us look at the conjuction "or".

Celine Dion is Canadian or Faith Hill is American. {1,1} = 0
Celine Dion is Canadian or Faith Hill isn't American. {1,0} = 1
Celine Dion isn't Canadian or Faith Hill is American. {0,1} = 1
Celine Dion isn't Canadian or Faith Hill isn't American. {0,0} = 0

With the conjunction "or, we see that only one of the independent clauses must be true for the entire sentence to be true. Though "or" is a conjunction (it connects independent clauses), we can also call it a disjunction because sentences with "or" are true only when one of the clauses is true. Now let us look at the conjunction "but".

Celine Dion is Canadian but Faith Hill is American. {1,1} = 1
Celine Dion is Canadian but Faith Hill isn't American. {1,0} = 0
Celine Dion isn't Canadian but Faith Hill is American. {0,1} = 0
Celine Dion isn't Canadian but Faith Hill isn't American. {0,0}= 0

The conjunction "but" appears to behave the same as the conjunction "and". However, this is not always the case. Compare these two sentences:

Celine Dion is Canadian and Bryan Adams is Canadian. {1,1} = 1
Celine Dion is Canadian but Bryan Adams is Canadian. {1,1} = 0

Though the two clauses connected by "but" are true, the sentence is false. Why is this? The reason is that the two clauses contain the same verb and same adjective. This makes the sentence false because "but" signals a contrast. The verb phrases of each clause must be different. Here is another example:

Celine Dion isn't American and Bryan Adams isn't American. {1,1} = 1
Celine Dion isn't American but Bryan Adams isn't American. {1,1} = 0

The sentence with "but" is false because both clauses contain the same verb and the same adjective. The verb phrases are the same. Since "but" signals a contrast, the verb "isn't" and the adjective "American" cannot appear in both clauses if the sentence is to be true. The verb phrases need to be different.

The following sentence normally sounds better when it is connected by "and".

Celine Dion isn't American and Bryan Adams isn't Australian. {1,1} = 1
Celine Dion isn't American but Bryan Adams isn't Australian. {1,1} = 0
Celine Dion isn't American but Bryan Adams isn't Australian. {1,1} = 1 in a specific context.

Without a specific prior context, the sentence above is false. However, it can be true if it negates a sentence such as the following: Celine Dion isn't American and Bryan Adams is Australian. This sentence could have been uttered to counter the previous sentence "Celine Dion is American and Bryan Adams is Australian". However, this situation is rather unlikely, so we can argue that in most situations it would be false.

The following sentence is absolutely fine:

Celine Dion isn't American but Faith Hill is American.
but {1, 1} = 1

The rules for "but" need to be refined. Here they are:

{1,1} = 1 if the two clauses contain contrasting information such as the verbs "is"/"isn't" or if they contain different adjectives.

{1,1} = 0 if the two clauses contain the same information such as the verbs "is"/"is" or the same adjectives.

We can state the rules for "and", "or" and "but" like this:

and

{1,1} = 1
{1,0} = 0
{0,1} = 0
{0,0} = 0

or

{1,1} = 0
{1,0} = 1
{0,1} = 1
{0,0} = 0

but

{1, 1 with a structure in each clause that fails to express an overall contrast } = 0
{1, 1 with a structure in each clause that manages to express an overall contrast } = 1
{1,0} = 0
{0,1} = 0
{0,0} = 0

These rules help to express the relationship between independent clauses and their respective coordinating conjunctions. The conjunction "and" needs to connect similar clauses to be true. The conjunction "or" requires that only one of the clauses be true and "but" requires that the two clauses express a clear contrast for the sentence to be true.