Problem 513 (10 points) Write a proof sequence for the following assertion. Justify each step. P prr =..q qrur **************$*$$*$***************$*$$*$**$***************$*$$*$***************$*$$*$**$*$ Problem 618 (10 points) Write a proof sequence for the following assertion. Justify each step. d (p A sq) Iq : |P ***$**********$*$$******$**********$*$$*$****$*************$*$$*****************$*$$******$ September 8, 2021 Assignment 1 (Part 212) of CSC 281 (F21, Dr. Zuo) Page 2 of 2 ***$**********$*$$*****************$*$$*$**$***************$*$$*$***************$*$$*$**$*$ Problem 718 (10 points) In the domain of all people, let P(x) be the predicate \"x is nice.\" Write the following statements in the symbols of predicate logic. (1) No people are nice. (3) Some people are not nice. (2) All people are nice. (4) Some people are nice. $$$$$e*$******$*$$*$**$*$$**$$*****$*$$*$***e*$************$*$*****$$$$$$$$$$$$$$$$$$$$$$$$ Problem 8/8 (15 points) Let the following predicates be given. The domain is all people. - R(x) = \"x is rude.\" - C (x) = \"x is a child.\" (1) Write the following statement in predicate logic: There is at least one rude child. (2) Formally negate your statement from (1) and write down its ultimate form. (3) Write the English translation of your negated statement