MATH EXPERTS. HElp me solve this and try to explain.?

Question

1. List all three-element subsets of A = {1, 2, 3, 4, 5}

Answer 1

Make a chart with all the numbers in the set across the top. Below each number in each column, write the next two numbers in the series (now you have 5 columns of 3 rows of numbers). Do that again and again and again until you come back to the original number. Now do it all over again for the 3rd row. Copy (vertically) all the sets of 3 numbers. This is the NON-mathematical way to get all the sets (NOTE: These are all 3-element subsets of your set WITHOUT REPITITION...if you are required to include repeating numbers, [111,222,121, 223, and on] there is a BUNCH more).

The mathematical way is a little easier; You need to find all sets of 3 numbers from a set of 5 numbers. Use the statistical (also seen in probability functions) formula of G(n,k) = n! / {k! (n-k)!}. Where n=numbers in the set (5 in your case), s=number of elements in the subset (3 in your case). Plug in these numbers and you get 5! / (3!2!) = 10

Answer 2

Here's a start:

1, 2, 3
1, 3, 4
1, 4, 5
2, 3, 4

etc... (I did NOT list them all.)

(The set of A contains 5 numbers - 1, 2, 3, 4, 5. A three-element subset means all groups of 3 of those numbers.)

Answer 3

The slope is the substitute in y divided with the help of the corresponding substitute in x. The substitute in y is: 5 - 2 = 3 The corresponding substitute in x is: 2 - a million = a million So the slope is 3/a million = 3 The equation of the line is of the type y = mx + c, and from above, m = 3, so y = 3x + c. whilst y = 5, x = 2, so 5 = 3 x 2 + c, so 5 = 6 + c, so c = -a million, and y = 3x - a million. verify: Take x = a million from the different pair of cordinates: y = 3 x a million - a million y = 3 - a million y = 2, so the answer is right. 2(3n + 10) = 5(4 - 2n), so 6n + 20 = 20 - 10n, so 16n = 0, so n = 0. x^2 + x - 6 (x + 3)(x - 2)

Answer 4

To tell how many you need to list, you need to do a combination of choosing 3 elements from 5 elements.
C(5,3) = 5! / [3! 2!] = 10
So you will need to list 10 sets.
{1,2,3}
{1,2,4}
{1,2,5}
{2,3,4}
{2,3,5}
{1,3,4}
{1,3,5}
{3,4,5}
{1,4,5}
{2,4,5}

Answer 5

B={3,4,5} Pythagorean triplet
C={1,3,5}Odd numbers
D={1,2,3},{2,3,4},{3,4,5}Arithmetic progression
Working on more...