only need parts (d) (e) and (f) ### Educational Resource on Venn Diagrams#### Venn Diagram RepresentationThe Venn diagram contains two intersecting circles labeled $A$ and $B$, set inside a universal set $U$. The elements are distributed as follows:- Set $A$ contains two regions: one with 12 elements and the intersection with $B$ that has 3 elements.- Set $B$ contains two regions: one with 15 elements and the intersection with $A$ that has 3 elements.- The region outside both sets $A$ and $B$, within the universal set $U$, contains 20 elements.#### ExercisesFind the following using the Venn diagram:(a) $ n(A \cap B) $ [ ](b) $ n(A^c \cap B^c) $ [ ](c) $ n[(A \cap B)^c] $ [ ](d) $ n(A^c \cup B^c) $ [ ](e) $ n[(A^c \cap B^c) \cup (A^c \cap B)] $ [ ](f) $ n(U^c) $ [ ]#### Explanation of Terms- $ n(A \cap B) $: Number of elements in the intersection of sets $A$ and $B$.- $ A^c $: Complement of set $A$, elements not in $A$.- $ B^c $: Complement of set $B$, elements not in $B$.- $ n(A^c \cap B^c) $: Number of elements in the intersection of complements of $A$ and $B$.- $ n[(A \cap B)^c] $: Number of elements not in the intersection of $A$ and $B$.- $ n(A^c \cup B^c) $: Number of elements in the union of complements of $A$ and $B$.- $ n(U^c) $: Number of elements outside the universal set $U$, typically zero if \(U\

Name: only need parts (d) (e) and (f) ### Educational Resource on Venn Diagr
Uploaded: 2024-03-05T11:53:49.000Z
Channel: Bartleby
Description: only need parts (d) (e) and (f) ### Educational Resource on Venn Diagrams#### Venn Diagram RepresentationThe Venn diagram contains two intersecting circles labeled $A$ and $B$, set inside a universal set $U$. The elements are distributed as fol

Here, n(A)=12n(B)=15 Total number of elements are,n(U)=20+n(A)+n(B)=20+12+15=47

Answered: Refer to the following Venn diagram. 12…

Math

Probability

Refer to the following Venn diagram. 12 A B 15 20 U Find the following. (a) n(A n B) (b) n(A° n Bº) (c) n[(A n B)°] (d) n(A° U Bº) (e) n[(A n Bº) U (A°n B)] (f) n(U^)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Vy - y 3 b) dy 2 y²

Q: Hi, Can you help me with parts, (d), (e), and (f)?

A: If a function f(x) is continuous on a closed interval [a,b] then f(x) attains both minimum and…

Q: If 2x + 3y = 4² then (x, y, z) = ? x, y, z e Z

A: A set of integers represented by symbols ZZNon negative set of integer is Z+

Q: Find u − v, 2(u + 3v), and 2v − u. u = (6, −7, 8, 3), v = (−2, , 7/3, −8/3 , −1)

Q: Solve for the following: a) Var(2X−5) when X ∼ U {1,2,…,20}. b) Var(3X−4) when X ∼ U {1,2,…,30}.

A: Given,X~U(1,2,.....20)minimum value=1maximum value=20f(x)=120-1f(x)=119 ; 1≤X≤20

Q: iv) (x+ yi)(3i + 2) = (2x – 3y) + (3x + 2y)i %3D

A: The detailed solution is given below Thank you

Q: Find f"-1) if f3) = (3x + 1)° . %3D O a) 9 O b) -27 c) 36 O d) -9

A: Given function is f(x)=y = (3x+1)3 We have to find f'(-1)

Q: S(3x + V-) dx (b) Evaluate : ) dx

Q: (d) 12 2

A: Given, A=132-1

Q: Are any of these expressions are valid? State your reason for each. If an expression is invalid, you…

Q: ラ f(zx-1)= 4×+3 メ=? f "(x)+ flx) = 15 B)-1 c)O 0) 2 E) 4 A) -2

Q: V(A - B) = A x (V x B) + B x (V x A) + (A - V)B + (B V)A,

Q: Let x be the r.v Such that ECx)=D2 ECx)=2a %3D [2+Qx}?) =2a3 %3D Findthe Value of a

Q: f and g functions 1-1 and cover fog (x) = 2g (x) + 3 since it is, how much is f (2)? A) 4 B) 5 C) 6…

A: See attached file for a step by step explanation.

Q: True or false: If (a,b) = (a,c) = 2, then (b,c) = 2

A: a, b=a, c=2

Q: a = (12,2) + -(4,5) = (12,2) + (-4,-5) = a%3D %3D %3D

A: Using addition of two points.

Q: Find x, y, z, and w. x 8 (2x- 1) (2x - 3) 7y (w + 1) (6y + 5) X = y =

A: Given x82x-1y67y=2x-3z55w+16y+5.

Q: (a) div (g) = Ag clas div (fDg) = \f • Dg + f Ag Show that

Q: Evaluate A (r 2") by parts.

Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: 이) (x-1) (X-2) 의1 +J- X

Q: Solve for w where u = (1, 1, 0, -1) and v (0, 3, -1, 2). w + 4v = -3u %3D

Q: Find u v, uu, ||u||2, (u v)v, and u. (2v). u = , V = (a) u. V 27 (b) 306 (c) 306 (d) (e) u u ||u||²…

Q: 3. (D5 –Dª – 2D³ +18D² –31D+15)y =0

A: Given differential equation is D5-D4-2D3+18D2-31D+15y = 0

Q: I+1 dr

Q: d(a, C) := ínf d(a, x)

Q: ) fx)= 3x"+会

Q: (z In z + 5)dz

Q: u = ⟨−7, −1⟩, v = ⟨−4, −1⟩, find (a) u ∙ v, (b) u ∙ u, (c) || v ||2 , (d) (u ∙ v)v, and (e) u ∙…

A: Hey, since there are multiple subparts are posted, we will answer first three subparts.

Q: A = ງ [3 123 212 51 [3 L6 _ [5 21 B = 4 1 _ _ [3 -21

A: We are asked to do the matrix operatios

Q: (Z7, e).

A: Addition Modulo n Let n be positive integer greater than one and a, b , where Z= {0, 1, 2, ……., n-1}…

Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Topic Video

Question

only need parts (d) (e) and (f)

### Educational Resource on Venn Diagrams

#### Venn Diagram Representation

The Venn diagram contains two intersecting circles labeled $A$ and $B$, set inside a universal set $U$. The elements are distributed as follows:
- Set $A$ contains two regions: one with 12 elements and the intersection with $B$ that has 3 elements.
- Set $B$ contains two regions: one with 15 elements and the intersection with $A$ that has 3 elements.
- The region outside both sets $A$ and $B$, within the universal set $U$, contains 20 elements.

#### Exercises

Find the following using the Venn diagram:

(a) $ n(A \cap B) $
    [ ]

(b) $ n(A^c \cap B^c) $
    [ ]

(c) $ n[(A \cap B)^c] $
    [ ]

(d) $ n(A^c \cup B^c) $
    [ ]

(e) $ n[(A^c \cap B^c) \cup (A^c \cap B)] $
    [ ]

(f) $ n(U^c) $
    [ ]

#### Explanation of Terms

- $ n(A \cap B) $: Number of elements in the intersection of sets $A$ and $B$.
- $ A^c $: Complement of set $A$, elements not in $A$.
- $ B^c $: Complement of set $B$, elements not in $B$.
- $ n(A^c \cap B^c) $: Number of elements in the intersection of complements of $A$ and $B$.
- $ n[(A \cap B)^c] $: Number of elements not in the intersection of $A$ and $B$.
- $ n(A^c \cup B^c) $: Number of elements in the union of complements of $A$ and $B$.
- $ n(U^c) $: Number of elements outside the universal set $U$, typically zero if \(U\

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Permutation and Combination$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.