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.

Tim's phone service charges $26.39 plus an additional $0.21 for each text message sent per month. if tim's phone bill was $31.64, which equation could be used to find how many text messages, x, tim sent last month?

Each person in an it department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. how many people work on system security and program implementation?

2x minus y equals 6, x plus y equals negative 3