Math 1350 Activity 2(Chapter 2)(Due by EOC Sep. 25) Group#_____

How do you turn the set ,arms legs into the empty set?

Given the following sets, find each intersection or union as requested. Note: Some of the unions

and intersections are given in terms of the original sets. Match your answer with the lettered

answers below, and place the letter in the corresponding box at the bottom of the page to get

the answer to the riddle.

4, 2,0,2,4A= − − , 5, 3, 1,0,1,3,5B = − − − , 5, 4, 3, 2, 1,0C = − − − − − , 0,1,2,3,4,5D =

1) A B 2) A C 3) C D 4) A B

5) C D 6) ( )A D C 7) ( )C D A 8) ( ) ( )A D A B

2,4,6,8,A= , 1,3,5,7,B = , 3,6,9,12,C = , 5,10,15,20,D =

9) A B 10) C D 11) A B 12) A C

0,1,2,3,A= , 0, 1, 2, 3,B = − − − , 1 1 12 3 4, ,C = , , 3, 2, 1,0,1,2,3,D = − − −

13) A B 14) A B 15) A D 16) C D

17) A B 18) B C 19) B C 20) ( )A C B

I. A B. B G. C N. D

M. 0 E. or L. 1,2,3,4,5 O. 1,2,3,4,

R. 4, 2,0− − T. 0,2,4 S. 5, 4, 3, 2, 1,0,1,2,3,4,5− − − − − V. 15,30,45,60,

Y. 6,12,18,24, Z. 0,4,8,12,

19 12 6 9 1 11 10 15 14 18

7 8 4 13 17 3 20 16 2 5

A B

C

U

A college professor asked his class of 42 students when they had studied for his class the

previous weekend.

9 studied on Friday

18 studied on Saturday

30 studied on Sunday

3 studied on Friday and Saturday

10 studied on Saturday and Sunday

6 studied on Friday and Sunday

2 studied on Friday, Saturday, and Sunday

Complete the Venn diagram of the survey and answer the following questions.

1. How many students studied only on Sunday?

2. How many students studied on only one day?

3. How many students studied on exactly two days?

4. How many students didn’t study on the previous weekend?

Friday

Saturday

Sunday

2

U

The following figures consist of congruent line segments(sticks). Unless otherwise stated, you

are not allowed to remove a stick completely.

1. Move just one stick to make a correct statement. (Try to find at least two different solutions!)

2. Arrange 4 sticks to make 15.

3. Move just one stick to make a correct statement.(Try to find at least two different solutions!)

4. Move just one stick to make a correct statement. (Try to find at least two different solutions!)

5. Remove 3 sticks to make a correct statement.

6. Remove seven letters from the following sentence so that it is still a true statement.

FIVE PLUS SIX PLUS SEVEN EQUALS EIGHTEEN

{Look for Roman numerals.}

7. Add 5 sticks of any size to make 9.

The numbers above are related to the famous Problem 79 of the Rhind Papyrus which dates from 1650 BC. It states that there are seven houses; in each house there are seven cats; each cat eats seven mice; each mouse eats seven ears of spelt; each ear of spelt produces seven hekat of grain. Find the total number of items involved. So what’s the answer?_________ It is believed to have inspired the following famous nursery rhyme riddle. As I was going to St Ives. I met a man with seven wives. And every wife had seven sacks. And every sack had seven cats. And every cat had seven kits. Kits, cats, sacks, and wives, how many were going to St Ives ? So what’s the answer?_________

1. The sum of the digits of a two-digit number is 7. The number is five times the units digit.

Find the number.

{Hint: Check the list of possibilities or use algebra. Possibilities: 16,25,34,43,52,61 or solve

7t u+ = and 5 10u t u= + .}

2. The sum of the digits of a two-digit number is 10. The number is 2 less than eight times the

units digit. Find the number.

{Hint: Check the list of possibilities or use algebra. Possibilities: 19,28,37,46,55,64,73,82,91

or solve 10t u+ = and 10 8 2t u u+ = − .}

3. The sum of the digits of a two-digit number is 12. The number is 20 more than eight times

the tens digit. Find the number.

{Hint: Check the list of possibilities or use algebra. Possibilities: 39,48,57,66,75,84,93 or

solve 12t u+ = and 10 8 20t u t+ = + .}

4. The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is

9 larger than the original number. What is the original number?

{Hint: Check the list of possibilities or use algebra. Possibilities: 18,27,36,45,54,63,72,81 or

solve 9t u+ = and 10 10 9u t t u+ = + + .}

5. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number

is 63 larger than the original number. What is the original number?

{Hint: Check the list of possibilities or use algebra. Possibilities: 29,38,47,56,65,74,83,92 or

solve 11t u+ = and 10 10 63u t t u+ = + + .}

6. The sum of the digits of a three-digit-number is 6. The tens digit is one less than the ones

digit. If the digits are reversed, the new number is 198 larger than the original number. What

is the original number?

{Hint: Check the list of possibilities or use algebra. Possibilities: 501,312,123, or solve

6h t u+ + = , 1t u= − , and 100 10 100 10 198u t h h t u+ + = + + + .}

6 2 8 4 5

6

1 8

3

9

2

6 2 8 4 5

6

Write the answer to each problem in the blank to the right. Use the

Decoder to solve the riddle by filling in the spaces at the bottom of the

page.

Write the answer to each problem in the blank to the right. Use the

Decoder to solve the riddle by filling in the spaces at the bottom of

the page.

Solve for the unknown base(s).

1. 35 120b= 2. 41 27six b=

3. 52 34seven b= 4. 32 44b=

5. 57 10eight b= 6. 31 11four b=

7. 15 30a b= 8. 28 34b=

9. 28 26b= 10. 23 43twelve b=

11. 20bXY = , 6X Y+ = , and 2Y X− =

8

, two of each. He claimed that he could determine the mass of any

whole kilogram of meat between 1 and 80 kilograms.

Think about base 3 numerals.

Can he determine the mass of any whole kilogram of meat from 1 to 40 kilograms, if he only

has one of each mass? Try to balance the following using the first three as a guide.