Math Is Fun Forum

owenflo

Member

Registered: 2014-07-21

Posts: 115

Conditional Statements and Venn Diagrams PLEASE HELP

PLEASE HELP
FOR 15 I GOT F

For problems 11 through 12, your complex statement is "Small pinpricks of light in the night sky are stars."

11. The converse of the statement is:

AIf it is a small pinprick in the night sky then it is a star.
BIf it is not a star, then it is not a small pinprick in the night sky.
CIf it is not a small pinprick in the night sky, it is not a star.
DSmall pinpricks of light in the night sky might be satellites.
E If it is a star, then it is a small pinprick of light in the night sky.
F A really cool sneaker.

12. "Small pinpricks of light in the night sky might be satellites" is a(n)

AConverse
BInverse
CContrapositive
DCounterexample
E Contraverse
F Statement

For problems 13 through 14 your complex statement is "Baseball players are athletes."

13. Which of the following is accurate?

AThe inverse of the statement is "If someone is a baseball player then someone is an athlete."
BThe statement is "If someone is an athlete, then they are a baseball player."
CThe statement can never be true.
DBaseball players all have great teeth and gums.
E The inverse of the statement is not true.
F The converse is: "Joey is a baseball player, and he is not an athlete."

14. What is q?

ASomeone is an athlete.
BSomeone is a baseball player.
CAll baseball players are athletes.
DAll athletes are baseball players.
E Baseball player
F Athlete

For problems 15 through 20, create Venn Diagrams to help you solve the problems. These are not easy diagrams, take your time and think through this carefully.

Hints on 15 (highlight the following paragraph with your mouse to see them, they are in the form of questions you'll need to answer):
<start highlighting here> You aren't meant to find out how many students are in the individual courses. How many students are you supposed to have counted? How many wound up being counted? What does the overage mean? How many times too many was a student counted if he was in all three classes?<end highlighting here>

15. 500 students are enrolled in at least two of these three classes: Math, English, and History.  170 are enrolled in both Math and English, 150 are enrolled in both History and English, and 300 are enrolled in Math and History.  How many of the 500 students are enrolled in all three?

A300
B330
C200
D120
E 90
F 60

16. 30 people are having lunch at my house.  16 of them want salads, 16 of them prefer pasta, and 11 of them want steak.  5 say they want to have both salad and steak, and of these, 3 want pasta as well.  5 want only steak, and 8 want only pasta.  How many people want salad only?

A3
B4
C16
D7
E 11
F 5

Make a Venn Diagram from the following information to answer questions 17 through 20:

25 students played soccer

4 boys played soccer and baseball

3 girls played soccer and baseball

10 boys played baseball

4 girls played baseball

9 students played tennis

3 boys played soccer and tennis

3 girls played soccer and tennis

3 boys played baseball and tennis

1 girl played baseball and tennis

1 boy played all three sports

1 girl played all three sports

Hints on the diagram (highlight the following paragraph with your mouse to see them):
<start highlighting here> Notice that the counts don't make sense as they are, because they're all inclusive. The soccer count includes every who plays soccer, even the students in the soccer and baseball, soccer and tennis, and the all three sport counts. The count for soccer and baseball includes the students who play all three sports. So you'll need to correct from the inside outward...first subtract the boy and girl who play all three sports from all the other counts, then subtract the dual-sport counts from the single sport counts.

Put another way, this is like the gecko problem--the entire soccer circle including the soccer and baseball students and the soccer and tennis students and the students who play soccer and baseball and tennis, will add up to 25.<end highlighting here>

17. How many students played soccer, but not baseball or tennis?

A4
B25
C12
D6
E 14
F 9

18. How many students played soccer and baseball, but not tennis?

A5
B10
C3
D4
E 7
F 13

19. How many students played just one of the three sports?

A1
B20
C13
D7
E 15
F 5

20. How many girls played only baseball?

A7
B2
C3
D4
E 10
F 1

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

hi owenflo

I agree with your answer for Q15. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Can you please help me with the rest

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

hi owenflo

Let's deal with the other Venn diagram questions first.

What I did for Q15 is this:

(1) Draw three overlapping circles and label them for maths English and history.

(2) Put zero in the three only_one_subject regions.

(3) Write x for the middle region (where all three circles overlap).

(4) Write 170-x , 150-x, and 300-x for the two subject regions.

(5) Form an equation by adding these and putting it equal to x.

(6) Solve for x.

Try a similar method for Q16 and post what you get.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

11.C
12.F
13.B
14.E
16.A
17.B
18.F
19.B
20.C

thanks for your help

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Hi owenflo

Do I detect a set of Compuhigh questions ? 

I would rather you had just tackled Q16 first.

I’ve looked at all your answers and I’m sorry to have to say I only agree with Q19.  Let’s just try to get Q16 right.  Then we’ll progress to 17-20.  These are tough as the diagram is much more complicated.  But I have a dodge that will make it easier.

Here’s my diagram for Q16.  Three set Venn diagrams have 8 regions: one region for all three sets overlap; three regions where only two overlap; three where the region is only in one set; and finally, the outside = not in any of the sets.

I write in a region if I know its number.  For the whole set I write the number on the edge of the circle.

Note that I did not write in " 5 say they want to have both salad and steak " because that is more than one region (salad overlap steak) but, once I had all three I could go back and fill in the number for salad + steak but not pasta.

You can work your way round the diagram, filling in the numbers in the order a, b then c.  The number you write for c is the answer to the question.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

i am really confused with how to do this? please explain.. sorry im terrible at math

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

I have colour coded the regions so it is easier to see which one I am talking about. (look back at post 6)

5 say they want to have both salad and steak, and of these, 3 want pasta as well. 

So there are 3 who want salad, steak and pasta.  Put that number in the region where all three circles overlap (yellow).

5 subtract 3 leaves 2, who want salad and steak but not pasta.  So put 2 in the region where salad overlaps steak without pasta (orange)

5 want only steak.  That number goes in the only steak region at the bottom (green)

So now we have three out of four regions making up the steak circle.  But there has to be 11 in total so you can work out the fourth number, a (grey).

8 want only pasta, so you can enter that number in the region on the right (red).

Now you know three out of four regions for pasta, so you can work out the last pasta region, marked with a 'b' (blue).

That gives three out of four of the salad regions so you can work out c (white).

You can check that you have all the correct numbers because they should add up to = 30 people are having lunch .   

How many people want salad only?  That is the last number you entered on the diagram, c.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

would #16 be only 2 people want salad?????
if so thank! and yes this is compuhigh

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Im sorry, *3 people want salad

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Please post your answers for this question like this:

a = ?

b = ?

c = ?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

a= 5
b=4
c=8

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

hi owenflo,

a cannot be 5.  The four numbers in the steak set must add up to 11.  You have 3 + 2 + 5 + a = 11.

The answer to b depends on getting a right so I'm surprised you got b correct, but you did.  Well done.

So the four numbers for salads must add up to 16.  You have 2 + 3 + b + c = 16

Have a look here:

http://www.mathsisfun.com/sets/venn-diagrams.html

Once you have Q16 right, I'll make up another to practise before we try the rest of the questions set by Compuhigh as they are harder.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

a=1
b=4
c=7
????

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Just a question but we went right to Q16 when I still have 11-20 and only got 15 and 19 right... maybe we should have started with 11

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

hi owenflo,

Good news!  Those answers are all correct.  So c is 7 and that is letter D in Q16.

When we started you had question 15 correct, so I wanted to work with what you can do first; intending to come back to the 'right_words_in_set_theory questions at the end.  I don't think it matters that we have missed them for now.  Knowing what those words mean won't help you with Venn diagrams anyway.

Let's practise with another question.

24 pupils are asked about which lessons they like.  Altogether 14 say they like maths; 12 like science and 15 like English.  7 say they like both science and maths, of whom 4 like English as well.  1 says he only likes science and 5 say they only like English.

Draw a Venn diagram and enter the information given.

Work out

(a) How many like science and English but not maths?

(b) How many like English and maths but not science?

(c) How many like only maths?

As a final check make sure that you have 24 pupils on your diagram.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

a=6
b=14
c=4

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Here is the diagram I started with:

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

a=3
b=1
c=4

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

need to finish this lesson as soon as possible, so can you please help me when you can.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Science = 12 so the 4 regions inside the science circle should add up to 12

You have 4 + 3 + 1 + 3 ≠ 12

I've made a new diagram that may help:

You could print a copy or just draw it on a sheet of paper.

There are 8 regions and 8 descriptions.  Can you match them?

need to finish this lesson as soon as possible, so can you please help me when you can.

I'm in the UK.  I usually check MIF when I get up at about 7 UT.

I'll go quicker but you have got to understand what you are doing or there's no point in me helping.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

A & B not C = 4
A & C not B = 7
A & B & C = 8
Only C =4
B & C but not A = 5
Only B = 1

????

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

For Q11 I got E, If it is a star, then it is a small pinprick of light in the night sky.
Is that correct?
E for Q11?

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Q12 B?
Inverse

owenflo

Member

Registered: 2014-07-21

Posts: 115

Re: Conditional Statements and Venn Diagrams PLEASE HELP

Q13, B? Sorry for so many posts