Give a recursive definition of each of these sets of ordered pairs of positive integers. [Hint: Plot the points in the set in the plane and look for lines containing points in the set.] a) S = {(a, b) | a ∈ Z+ , b ∈ Z+ , and a + b is odd}

(2,1), (1,2) is your base step

if (a,b)   is in the set (a+1,b+1) will be in  the set

if  (a,b) is in the set (a+2,b) will be in the set

if (a,b) is in the set (a,b+2) will be in the set.

Step-by-step explanation:

Think about how to solve this problem in general. How can you assure that the sum a+b is odd ?

Think about this, what happens when you sum two even numbers ? The result is even or odd ?

2+6 = 8 (even  )

10+12 = 22 (even)

And what happens when you sum two odd numbers ? The result will be even or odd ?  Look

3+7 = 10 (even)

5+11 = 16 (even)

Therefore to assure that a+b is odd, one of them has to be odd and one of them has to be even, that is why

(2,1), (1,2) is your base step

if (a,b)   is in the set (a+1,b+1) will be in  the set

if  (a,b) is in the set (a+2,b) will be in the set

if (a,b) is in the set (a,b+2) will be in the set.

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew