Remember to follow the guidelines I laid out for proving claims about subsets in the lectures and in the notes. In particular, do not use modus tollens, the contrapositive, or de Morgan's laws to bypass proof by contradiction When it comes to subsets and set operations, the only facts you can use are the rules of natural deduction and the following definitions Here are the definitions about sets that you will need for these proofs: Definition. x E An B means that x E A and r E B. Definition. x E AU B means that x E A or x E B. Definition. x E A\ B means that x E A and x f B. Definition. x E A means that x £ A. Definition. ACB means that every member of A is also a member of B 1. For the following claims, first decide if they are true or false. If they are true, then give an informal proof of the claim. If they are false, then give a counterexample that disproves the claim (a) For all sets A and B: AUBCA (b) For all sets H, I, J, and K: if H C I and J C K, then (Hn J)C (In K) (c) For all sets A, B, C, D, and E: if AU B C C, then D\CCD\(An E) (d) For all sets A, B, and C: if A C C, then AUB CBUC (e) For all sets A, B, and C: if A C C, then AUBCBNC (f) For all sets X, Y, and Z: if (Xn Y) C Z, then X C Y n Z

Perform the indicated operation. (30 3-j19) (j2-1)

Please help me with these question. I am having trouble understanding what to do. Please show all your work. Please do every question. I am study for my exam. And i need to know if I got the correct answer. And shown the correct steps just do questions 3 & 4 Course: Discrete mathematics for CS Thank you

SOLVE STEP BY STEP IN DIGITAL FORMAT 3. Is the series 2n convergent or divergent? Hint: quotient criterion