Discrete math

[Jynx]

I've had a lot of work to do and I'm really stuck on these few.

1.) Chorus and Band at Henniger High School, 46 students sang in the chorus or played in the stage band, 30 played in the stage band, and 4 students sang in the chorus and played in the stage band. How many students sand in the chorus?

2.) In a survey of four-year colleges and universities, it was found that

356 offered a liberal arts degree
293 offered a computer engineering degree
285 offered a nursing degree
193 offered a liberal arts degree and a computer engineering degree
200 offered a liberal arts degree and a nursing degree
139 offered a computer engineering degree and a nursing degree
68 offered a liberal arts degree, a computer engineering degree, and a nursing degree
26 offered none of these degrees

a.How many four-year colleges and universities were surveyed?
Of the four-year colleges and universities surveyed how many:
b.A liberal arts degree and a nursing degree, but not a computer engineering degree?
c.A computer engineering degree, but neither a liberal arts

3.) Find the truth value of the statement ~[ p ? (q ? r) ]

4.) Determine whether the argument is Valid or invalid
q ? p
q____
~p

 

[Deleted member 4993]

I've had a lot of work to do and I'm really stuck on these few.

1.) Chorus and Band at Henniger High School, 46 students sang in the chorus or played in the stage band, 30 played in the stage band, and 4 students sang in the chorus and played in the stage band. How many students sand in the chorus?

2.) In a survey of four-year colleges and universities, it was found that

356 offered a liberal arts degree
293 offered a computer engineering degree
285 offered a nursing degree
193 offered a liberal arts degree and a computer engineering degree
200 offered a liberal arts degree and a nursing degree
139 offered a computer engineering degree and a nursing degree
68 offered a liberal arts degree, a computer engineering degree, and a nursing degree
26 offered none of these degrees

a.How many four-year colleges and universities were surveyed?
Of the four-year colleges and universities surveyed how many:
b.A liberal arts degree and a nursing degree, but not a computer engineering degree?
c.A computer engineering degree, but neither a liberal arts

3.) Find the truth value of the statement ~[ p ? (q ? r) ]

4.) Determine whether the argument is Valid or invalid
q ? p
q____
~p

Please share your work with us, indicating exactly where you are stuck - so that we would know where to begin to help you.

 

[Jynx]

I really hate to sound completely helpless here but I don't eve know where to begin. My book is full of problems but not explinations. Its the worst math book I've ever seen, it ask's a lot but doesn't break things down.

 

[mmm4444bot]

Regarding the first exercise, have you ever seen a Venn diagram?

We have two overlapping groups, so we can represent these groups by two overlapping circles.

[attachment=0:2n0jrmbb]Venn.JPG[/attachment:2n0jrmbb]

The circle on the left holds all students that participate in Chorus (C + 4).

The circle on the right holds all students that participate in Band (B + 4).

We are told that 4 students participate in both, so region C represents those who participate only in Chorus, and region B represents the number participating only in Band.

We are told that there are 46 singers in all.

We are told that 30 students total participate in Band (in other words, those who are in Band along with those who are in both).

B + 4 = 30

B + 4 + C = 46

You're asked for the value of C. Can you solve this system of two equations?

 

[Deleted member 4993]

Second problem is also Venn diagram - only more sections.

First find the number of colleges that offer at least one of the degrees. Then add 26 to it to find total number of colleges surveyed. These types of problems are generally taught in middle-school. If you are at higher grade - the book may have assumed that you should know these and these problems are put-up as refresher.

 

[somathysok]

Homework #4
Homework #4