Dear Tutor, Kindly provide me the answer with explanation, so that i will be more understand. Please show step by step for every calculation. Thank you in advance.

Course: Discrete Mathematics

I{Srluestion 1 i. Explain the relationship of domino effect with the mathematical Induction ii. Use Mathematical induction to prove the following proposition. \"\"'answer 2 questions from Part A AND all questions from Part Bm Part A i. 13+23+33+...+n3 2L4+1y ML}: +11}: + 2] 2. 1(1)+2(s)+3(4}+...+n(n+1)= 3 3. 2{l]+2(4)+2[?)+...+2{3H2)=3Hlr.a 4. 2+21+23+...+2\"=2[2"1] 5. 1(1r)+ 2(21}+ 3(3!)+. ..+ n[n1)={n+1)11 Part B Question 2 Define vour own set A with 8 numbers (example: Let A = { 3.2.l.,1,2,3.4}] \"*each group should define different set of A***Don't use Set A in the above example Let R be a binary relation on A such that? = {pay} xy :_=- D} i. Find the relation R ii. Determine the properties of R and state the reasons iii. Determine whether R is equivalence relation and state the reasons. If ves, find the equivalence class and partition iv. Determine vvhether R is partial order and state the reasons