Let’s talk about the connective called the

conjunction and, sometimes, we’ll just call this “and”. Now, in English, a conjunction

is used to join any two thoughts or ideas together. For us, it will just be when we

join two thoughts together with this idea of and, with this idea that we’re trying to

say both of the things are true. If I want to symbolize this, well, I always need two

statements to put together, so let’s say p this symbol q. I’m going to read this “p and

q” to let people know I’m talking about the conjunction and then, finally, some words

that mean conjunction

are and, okay, that’s the most common one, but is used to mean and, both of these things,

nevertheless, yet, still. Okay? Words that mean “this thing and also that thing” all mean

conjunction, all mean “and”. Let’s look at a couple of examples of symbolizing. Let’s let

p be the statement “It is after 9 pm.” and q be the statement “Tim is at work.” If I

want to symbolize “It is after 9 pm and Tim is at work.” I just need to break this down.

“It is after 9 pm” is my statement p. Tim is at work” is the statement q. This has

an “and” in the middle, so I’m going to use an “and”. So, it is after 9 pm and Tim is

at work is p and q. Okay? Pretty nice, pretty straightforward. Let’s look at this one. How

about “It is not after 9 pm but Tim is at work.” Okay, again, let’s start out here.

“It is not after 9 pm” is the statement not p. I would symbolize that not p because it

is the negation of that statement p. “Tim is at work” is still just the statement q.

And then, in the middle here, I’ve got “but”. “But” means the same thing as “and”. I’m saying

both of these things are true, I have maybe a little different implication when I hear

the English statement when I use “but” instead of “and”, but I’m still making the same statement.

Right? “It is not after 9 pm but Tim is at work” logically means the same thing as “It

is not after 9 pm and Tim is at work”. So, now I’ve got this, this starts with not p

and q. Notice that not p, this negation here, doesn’t need parentheses or anything, negations

are actually stronger than conjunctions, so I don’t need another set of parentheses or

any parentheses here. When I see not p and q, I know that the negation is just on this

p and then I’m going to take that and “and” it together with whatever q is. Alright, here’s

one more. I’ve got the same p is “It is after 9 pm” q is “Tim is at work” and my statement

this time is “Tim is not at work” okay “Tim is not at work” so this is the negation of

“Tim is at work” so this is not q. “Yet” means “and”. “It is after 9 pm” is the statement

p, so this would be symbolized not q and p. It’s tempting to write this as p and not q

just because we said “Hey, p was first, p is first alphabetically, p is the first thing

I know” and, technically, that’s equivalent to what we have written down, but if I’m going

to symbolize this statement, I should write these things in this order. Okay? In that

statement, not q is first, then I have my “and”, my conjunction, being represented by

“yet”, and then “it is after 9 pm” or p comes second. So I should write that as not q and

p.

Nice