Structural Induction Let S be the subset of the set of ordered pairs of integers defined recursively by:
Base case: (0,0) E S
Recursive step: If (a, b) є s, then (a + 1, b + 3) E S and (a +3, b+1) є s.
1) List the elements of S produced by the first four applications.
2) Use structural induction to show for all (a, b) E S that (a+b) = 4k for some k e Z.
Reminder: In other words (a +b) is divisible by 4.

step-by-step explanation:

ddd

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.