5

If 5 = (0,1.2 3,45.6.7, 91 and 00,2 B = (1, C={23.4, D = {1, the elements of the sets corresponding following events:AnB(COdjuB (Snch Ancnd' Draw Venn diagram ...

Question

If 5 = (0,1.2 3,45.6.7, 91 and 00,2 B = (1, C={23.4, D = {1, the elements of the sets corresponding following events:AnB(COdjuB (Snch Ancnd' Draw Venn diagram for each item.

If 5 = (0,1.2 3,45.6.7, 91 and 00,2 B = (1, C={23.4, D = {1, the elements of the sets corresponding following events: AnB (COdjuB (Snch Ancnd' Draw Venn diagram for each item.



Answers

If $S=\{0,1,2,3,4,5,6,7,8,9\}, \quad A=$ $\{0,2,4,6,8\}, B=\{1,3,5,7,9\}, C=\{2,3,4,5\},$ and $D=\{1,6,7\},$ list the elements of the sets corresponding to the following events: (a) $A \cup D$; (b) $A \cap B$; (c) $B^{\prime}$; (d) $\left(B^{\prime} \cap D\right) \cup A$; (e) $(S \cap D)^{\prime}$; (f) $A \cap C \cap D^{\prime}$.

Okay. So we're going to Find this 1 1st. This just means all of the elements that are in B. But not in not any elements from sea. So all of this here is excluded because that is sincere. We just want the elements that are only be So we're taking away everything from sea. Okay? And so now what we have is this left and so we have we need all of the elements in A. And none of the elements can be okay. So we don't want anything from P the rest. I was left with all needed. So that means that we're left with just A. The so this one we subtracted just took away. See we don't need to see. And then we're left with just two elements in B, C, X and C. And then we don't need to see it because we're subtracting again. Right? And so we're left with just two elements in it.

In this problem, let us first define what is over in diagram. Over in diagram is of pictorial representation to illustrate the relationship between different sets. No, Let us look at Part one, which is I. As a proper subset of B. So this is subset B. This is the set B. And this is sad, right? This is the main suspect. S. You see that all the elements of I within the elements of B and I is not equal to. Next look at in the the stormed sets, which means that intersection B. S. Fine, Which means that two sets do not have any intersection. This is A me and this is needless. Listen, look at my toe which is A. And B aren't not destroyed, which means that not this joint, which means that intersection B is some set, correct. The money is this? So you can see here that intersection B. Which is this has some what? That's all.

In this problem, Let us first look at part one where A. And B. Are any two sets. This now let's maybe the wind items. This is E. Mrs B. And your family is the whole region called just the union. Mm. Let's make an intersection. B. She's going to the smallpox mrs E. Being a inter sexually next let's make A minus B. Do you mind as we is just the spot. This is A. B. A minus B. Now let's make the compliment. This is A. This shouldn't be he complimented anything which is not A. Comes this region. Next we are given that. Mhm. As a proper subset of being this is B. And this is C. Now let's first find a union be you mean you're going to be nothing like this. This is speed. This is the intersection. We will be only the part. This is equally to be itself. And this is equal to it's next let's find A minus B. So Minister A minus B means that we're looking for a set of all elements which are in A but not. And we since is a proper subset of B. This is not possible. Let's look back or which says we want a compliment. This is B. This is A. He complimented all the region which is not. That's all. No, that the third part were India design sets, which means that intersection of years. Right? See this is B. A. Union B is nothing but individuals intersection. B. We already figured out is five. Next is this is A. This is V. And we are looking for a -7. A minus B means elements which are there in A. But not in B. Which is something. But it's next is this is A. This is B. And we are looking for a compliment. A compliment will be everything which is martin. That's all.

Yeah, so the probability of B given C equals zero tells us that if we are in B. Yeah, then C is nowhere near. Alright. Could be somewhere near it, but it's definitely not overlapping now, the probability of a given C is one would mean that, and if we are in C then we must be in A. So A is going to be the larger circle like this. Yeah, this would mean that the probability of a given C is one. So if she happens, then he has to happen as well.


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