Well for question one on problem set four, we have to choose which one of the

following is equivalent to to this expression.

Okay, we're negating a universally quantified statement in which there's

conditional. And we're told that there's only one of

these, one of these answers is correct. The correct answer, let me just jump to

the correct answer and then see what's wrong with some of the others.

Is, is part C, the notforall becomes an exist and the negation goes into this

part. When you negate a conditional, you end up

with the antecedent together with the negation of the consequent.

And when you negate the disjunction, the negations filter in, and the disjunction

becomes a conjunction. So if you follow the rules about, well

they're not rules, they're, but they sort of our rules.

But I, I recommend you not to think of them in terms of rules because that's,

that's not really getting at what this course is about.

but there's certainly patterns of activity that you can get to get to

recognize, and then what happens is universals become exists.

You have the truth of the antecedence, in place of an implication, of a conditional

you have a conjunction. And then when you negate these guys the

negation applies to each one and that becomes a conjunction.

Okay, but that, but as I used to indicate or I just referred to, really what I want

you to do is concentrate always on why it is that you get a behavior.

Why does this give you px and not that. Why does negating this give you a

conjunction there, so it's all about understanding.

and if you, if you simply learn to apply the rules, you really don't have a useful

skill, okay? Computers are good at applying rules.

That's what they do, that's all they can do.

People can go much beyond that. Okay, what's wrong with some of the

others. Well, the first one is just hopeless.

I mean, there's just nothing remotely like that.

If you got that as your answer, then either you were having either a temporary

aberration, or you really, really, really haven't got the issue with this.

The others, there were reasons why people could go wrong.

And the others were put in, because there were mistakes that people frequently

make. Okay, in the case of this one, the

negation is in the wrong place. when you negate a conditional, the

negation doesn't come together with this one.

The negation should come inference of here and inference of there.

So it's just ,um,mixing up where the negation comes in.

Okay, but, otherwise, zero place. So, so it's like applying your bis,

you're applying the right sort of, let me call it rule, you're doing the right

thing but you're, you're, you've got one step out.

It's like getting a negative sign, a minus sign in the wrong place in an

equation. looking at this one, well everything went

fine except you forgot to change disjunction to conjunction, but

everything else was fine. And in the case of this one, you forgot

to, then that should be conjunction, and everything else was fine.

Okay, so in cases b, d, and e, there was just one thing wrong.

It's even possible you just did that by a slip.

I mean, heaven only knows you've seen me make slips often enough in the, in the

lectures and the tutorials where I write the wrong thing down or I whatever.

It's uhh, you have to keep a lot in our minds when we're doing these things.

And frequently what a hand does isn't what we're thinking it's doing and

sometimes what we say, isn't what we think we're doing.

Mathematics is like that, when you're really focusing on the mathematical

concepts, in the heart of it. You can make slips with the writing and

with the wedge you. I do it all the time, and we all do.

That's, that's just part of thinking mathematics.

It takes a lot of concentration to focus on the mathematics.

And the, the every day things like writing and using words, tend to miss out

on that because our mind is focused on the content.