## Solution for problem 4.20 Chapter 4

# (a) Result 4.12 states: Let n Z. If n2 n (mod 3), then n 0 (mod 3) and n 1 (mod 3)

Mathematical Proofs: A Transition to Advanced Mathematics | 3rd Edition

(a) Result 4.12 states: Let n Z. If n2 n (mod 3), then n 0 (mod 3) and n 1 (mod 3). State andprove the converse of this result.(b) State the conjunction of Result 4.12 and its converse using if and only if.

**Accepted Solution**

**Step 1 of 3**

Math 1172 -Autum 2015 Nam Take Home Recitation Instructo Quiz 3 - SHOW ALL WORK!!! Unsupported answers might not isformed byrevolvingthe graphof y= 4c2for0 < x < 3 Problem 1 [4points] A tank (inmeters) about they-axis. the volume of the a) Ifthe tank isfilledith waterto thelevel(height)of hmeters, find water in termsof h. 2 3 water atthe rateof 2— atwhat rate isthe levelofthe water b) Ifthe tankislosing places.) fallingwhen the levelsat 1meter (Approximate to2 decimal

###### Chapter 4, Problem 4.20 is Solved

**Step 2 of 3**

**Step 3 of 3**

Enter your email below to unlock your **verified solution** to:

(a) Result 4.12 states: Let n Z. If n2 n (mod 3), then n 0 (mod 3) and n 1 (mod 3)