00:02
Once again welcome to a new problem.
00:05
This time we're dealing with sets.
00:08
And so when you think about sets, so a set is pretty much collection of elements.
00:16
So a set is a collection of elements.
00:18
For example the set a could have the elements 12345 and six.
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And the set b.
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You could also have the elements 123.
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Such that if b is less than the set a, we call b.
00:36
The subset of a.
00:40
The the other thing that happens is for example we could have two sets together.
00:47
And this is called a union.
00:49
And the reason why it's called the union is because we can either have either have elements elements of set a or b.
01:02
So we can either have both elements and then also a intersection.
01:08
B.
01:09
This is pretty much an intersection and it simply means that these are the elements of a.
01:20
And these are the elements of a.
01:24
And be.
01:25
So a minus b would be the elements not in the but um in a elements not indeed but in a.
01:42
And then uh a this is a compliment, this is a compliment and this simply means that elements present elements present in the universal universal set but uh not in a.
02:06
So these are the elements present in the universal set but they're not present in a.
02:14
And then this is the negation of p.
02:19
And this simply means not be, we also have a disjunction.
02:24
And when we talk about disjunction it's almost like a dis joint p or q.
02:32
We also have a conjunction when it comes to a conjunction, this is the same as and q.
02:40
So this is p and q.
02:42
That's a happens to be a conjunction.
02:46
And so but we also have identity laws.
02:52
And these are for propositions, identity laws for proposition.
02:58
So p and t.
02:59
You would be identical to pee.
03:02
This is the true statement.
03:05
And so if you combine the truth proposition with p proposition, you get the same thing and then oh, if this becomes identical to pee, remember we also have the domination laws for for positions.
03:30
So this is domination laws for propositions and this simply means that you have p or t is the same as the truth value and p and f is identical to a false statement.
03:48
So that shows the proposition.
03:51
When it comes to negation, we do have laws.
03:55
And the laws is that if you take p or the negation of p, you're going to get a true statement.
04:02
And if you get b and the negation of p, you're gonna get a false statement.
04:09
Of course we do have distributive properties.
04:14
And when it comes to distributive properties, you have p or q.
04:20
And r.
04:21
If you make the distribution you're going to get or q and um p o q and q...