Sets and Relations Questions and Answers

a Let char x 15 evaluate the expression x b Let char x 15 evaluate the expression x 1 c Let char x 5 evaluate the expression x 2 d Let char x 5 evaluate the expression x 1 1

4 on the set a b R c d necessary and sufficient condition for a b c d defined as R relation is given R Does the relation have the properties of reflection symmetry inverse symmetry and transition Please search

2 Investigate whether the following equations are true for any set a Ax B D A B A D b An BAC AB A AC

Use the matrix below Find a 21 A 63 10 00 35 2 5 44 in matrix A

LC Exercise Apply the BFGS method to the following functions with x a and H I Show that H 3 G a f x x 22 x 8 4 x b f x x 5323 x 0 1 x

5 Find the sum of the infinite geometric series if it exists If it doesn t exist explain why 00 1 n 1

22 14 39

What is the equation for the family of quartic functions with zeros 2 and 1 3 Check all that apply Oy k x 2 x 2 x 2x 2 k0 Oy k x 4 x 2x 2 k 0 y k x 4 x 2x 2 k 0 y k x 2 x 2 x 2x 2 k 0

A group of 2418 students were surveyed about the courses they were taking at their college with the following results 1034 students said they were taking History 1281 students said they were taking Dance 1064 students said they were taking English 581 students said they were taking Dance and English 575 students said they were taking Dance and History 462 students said they were taking English and History 262 students said they were taking all three courses Fill in the following Venn Diagram with the cardinality of each region Dance I 1281 IV 575 II 581 V 262 VII 1034 History English VI 462 III 1064 VIII

College classes Math 18 14 5 3 Science 8 History 19 13 How many students are taking math 20 D How many students are taking science and history How many students are taking math and science but not history

Write the vector shown below as a combination of vectors and shown above Vector u U 15

CAN STRUKTY Do you know what ills are Maybe look that term up before answering this question STLASE

Show that the rth moment about the origin of the gamma distribution is u Hint Substitute y Extract the constants out of the integral 8 S y 10 0 Simplify your answer H r I a X in the integral defining u and then use the gamma function to evaluate the integral How does p r x r I dy follow from this result OA The integral is the gamma function with argument o OB The integral is the gamma function with argument r OC The integral evaluates as p p r a r I a The integral is the gamma function with argument a r MILKUR W

Consider the Venn Diagram below that shows the number of elements in each set Use this information to answer the questions below 5 A 8 B 10 1 How many elements are in Set A How many elements are in Set B How many elements are in Set A and Set B How many elements are in Set A or Set B How many elements are not in Set A How many elements are not in Set B Vidas

Consider the Venn Diagram below A B n A 33 43 10 32 n AUB 55 n B 79 E Question Help 8 55 X Ou n AB 32 Ou Video 46

Let S 1 2 3 18 19 20 be the universal set Let sets A and B be subsets of S where Set A 3 4 5 6 8 9 10 11 12 13 14 18 Set B 4 5 6 7 9 10 11 12 15 16 17 19 20 Determine the following n A 12 n A n B 8 n An B 7 n AUB 18 13 X X 9

Problem 1 Let C 0000 1010 2020 0101 0202 1111 1212 2121 2222 be a linear code over F3 0 1 2 a List the cosets of C b Show that is a parity check matrix for C 1 0 2 0 132 01 02

The angle 8 is an integer e g 0 11 12 when measured in radians Give the radian measure of the angle It helps to remember 3 Q Q Ay

Determine whether the description given describes a permutation or a combination Jocelyn is the manager of a community college softball team The team has 16 players a Jocelyn selects 9 players for the batting order of today s game b Jocelyn selects 6 players to volunteer at the school s open house a The description Jocelyn selects 9 players for the batting order of today s game describes

Find the y intercept of the line 12 12 g 16 12

Blood tests of 100 people showed that 46 had the A antigen and 28 had the B antigen Another 40 had neither antigen and so are of type O How many people are of type AB having both the A and B antigens Draw and label a Venn diagram that shows the number of people with blood types A B AB and O How many people are of type AB having both the A and B antigens 14 c Which of the figures below is a Venn diagram that organizes people by bloodtype A AB B and O Fill in the values for each of the four regions Select the correct choice below and if necessary fill in the answer box to complete your choice OA OB O C 1 O I A II B III IV IV 1 0 CHE I A 11 IV B III IV 0 IV A 1 II B III IV

Draw a Venn diagram for the relationship An B U An C U U A A C C B B U U A A C C B B

Use set notation to identify the shaded region O Bn AUC OBUAUC O BUA nC OBU ANC OBn AVC U A C B 2

From a survey of 100 college students a marketing research company found that 50 students owned iPods 40 owned cars and 10 owned both cars and iPods a How many students owned either a car or an iPod but not both students b How many students do not own either a car or an iPod students

Use set notation to identify the shaded region OBn AUC OBn AUC O BUA nC OBU ANC BUAUC U A C B

Let U 1 2 3 4 5 6 7 List all the members of the given set Enter your answers as a comma separated list Enter EMPTY for the empty set x x is less than 5 n x x is greater than 5

Draw a Venn diagram for the relationship AUBnC O A A B B

Use set notation to identify the yellow shaded portion of the following Venn diagram U O O AUB O AnB O AUB AnB B

Consider the sets X and Y Write the statement in symbols The complement of the intersection of X and Y OXUY OXnY OXUY OXnY

erform the given set operation Let U 1 2 3 4 5 6 7 8 9 10 Enter your answers as a comma separated list Enter EMPTY POP the a 1 3 7 n 8 9 b 1 3 7 U 8 9 1 c 1 3 7 8 9

et U 1 2 3 4 5 6 7 B 1 2 4 6 and C 3 4 7 List all the members of the given set Enter your answers as a comma separated list Enter EMPTY for the empty set BUC

Use Venn diagrams to prove or disprove each statement Remember to draw a diagram for the left side of the equation and another for the right side If the final shaded portions are the sam you have proved the result If the final shaded portions are not identical then you have disproved the result An BUC An B n An C left side Venn diagram U C B B U A A B B

Let U 5 6 7 8 9 10 11 A 5 6 7 8 B 5 6 9 10 and C 7 9 11 List all the members of the given set Enter your answers as a comma separated list AUB nC

Consider the sets X and Y Write the statement in symbols A union of complements OXUY OXnY OXUY OXnY OXUY

Let U 7 8 9 10 11 12 13 A 7 8 9 10 B 7 8 11 12 and C 9 11 13 List all the members of the given set Enter your answers as a comma separated list AU BNC

In a survey of a TriDelt chapter with 50 members 23 were taking mathematics 31 were taking English and 8 were taking both How many were not taking either of these subjects members

Let U 1 2 3 4 5 6 7 A 1 2 3 4 and B 1 2 5 6 List all the members of the given set Enter your answers as a comma separated list Enter EMPTY for the empty set AUB x

Let U 2 3 4 5 6 7 8 and A 2 3 4 5 List all the members of the given set Enter your answers as a comma separated list Enter EMPTY for the empty set A

Draw a Venn diagram for the relationship XUY U U X OD Y OD U U X

X n for any set X OZ OW SON OX

A 15 B 10 5 C 10 5 D 2 E 2 3 a What is the cardinality of each set A B IC IDI E b Which of the sets are equivalent A B C D E OAB C D E ABD C E OAB C D E OABE D C 4 A c Which of the given sets are equal OA D E B C O A B D C E OC E O A B OD E

How many subsets does the set L 1 2 3 4 have subsets

List all possible subsets of the given set I 5 6 O 5 6 5 6 O 5 6 5 6 O 5 6 O 5 6 O 5 6

ecide whether each statement is true or false a a E m a t h O True O False b m E m a t h O True O False

Missing Amounts from Balance Sheet and Income Statement Data One item is omitted in each of the following summaries of balance sheet and income statement data for the following four different corporations Determine the missing amounts Hint First determine the amount of increase or decrease in stockholders equity during the year Freeman Heyward Jones Ramirez Beginning of the year Assets Liabilities End of the year Assets Liabilities During the year Additional issuance of capital stock Dividends Revenue Expenses 453 700 521 800 204 200 272 200 271 300 155 200 562 600 245 000 730 500 183 800 229 600 163 400 104 400 31 300 20 400 31 800 149 800 234 900 81 700 135 700 251 200 247 100 510 600 280 000 82 400 120 800 230 600 263 500

of a b is a b conjugate reciprocal

in diagram with 2 sets Unions intersections and Here is a Venn Diagram with sets A B and the universal set U Shade A U B on the Venn diagram U

The 12 shapes in the Venn diagram shown to the right are described by the attributes of shape size and color Let C H and T denote the respective sets of circular hexagonal and triangular shapes Similarly let S L R U and B denote the sets of small large red and blue shapes The set A contains the shapes that are small and not a triangle so A SOT Complete parts a through d below a Express small circles in symbolic form A Snc OB CUSUS OC CUS On soco A 4

Finish labeling the number of elements in the regions in the Venn diagram shown to the right where the subsets A B and C of the universe U satisfy the following conditions n U 100 n A 30 n B 50 n C 40 q S t 1 V W X 1 n ANB 16 n BNC 16 n ANC 18 n ANBOC 9

ler contains 100 ice cream bars There are 10 Vanilla bars 20 Mint Chocolate Chip bars 30 Chocolate bars and 40 Rocky Road bars If one bar is selected at random from mine the probability that the bar selected is Rocky Road Mint Chocolate Chip or Vanilla probability that the bar selected is Rocky Road Mint Chocolate Chip or Vanilla is Type an integer or a simplified fraction