Totally 6 questions and need explanations.

Need answers in 2 hours.

It’s best to write as a document.

2.5.9. For each statement, decide whether it is true or false. Justify your answer briefly.

(a) {(x, y): X,Y ER and

x – 1 = 0} < {(x, y): x,y ER and x2 – x = 0}
(b) {x ER: x3 – 2x = 0} CQ
(c) NER
(d) Z XR CR ~ Z
(e) N Z CQ XR
2.5.1. Let S = = {(x, y) E N2 : (2 – x)(2 – y) < 2(4 – 2 – y) }.
Prove that S=T, where T = {(1, 1), (1, 2), (2, 1), (1,3), (3, 1)}.
2.5.2. Let S = {2,3} ^{-2,-1,0}, and let T be the set of all ordered pairs (x, y) E Z Z such that
-2 < x + 2y