In testing the validity of logical expressions, conjunctive propositions use the word “and” while disjunctive propositions use the word “or”.
For starts, this question is more in the field of Philosophy and Logic than it is for English Grammar. But since at the current time we have a choice of English Grammar or some sort of set theory in the math categories (and I have no idea where those are)… here we are in English Grammar.
Ok. Let’s first talk about what a proposition is – it’s something that is expressed and about which we are going to determine it’s truth or falsehood . For example:
“Canada is in North America” expressed as a proposition would be given the result of “True” because indeed Canada is in North America.
“New York City is the biggest city in Canada” expressed as a proposition would be given the result of “False” because New York City is located in the United States.
Sometimes we want to express two or more statements and make a judgement on the whole expression. We see this in English with the use of the words “and” and “or”.
For instance, if we want to know that both propositions grouped together are true, we use the word “and”. This is called a conjunctive proposition. For instance:
“Canada is in North America and New York City is the biggest city in Canada.”
If either one of the individual propositions are False, then the whole thing is False. And since we know that one is False, indeed the whole thing is taken as False.
Other times, if we want to know that at least one of the propositions in the grouping are true, we use the word “or”. This is a disjunctive proposition. For instance:
“Canada is in North America or New York City is the biggest city in Canada.”
Now we have one proposition that is True, so the whole thing is seen as True.
The link below has a great introduction into Logic, including symbols, other uses of language that indicate conjunctive and disjunctive propositions, and the like: