Let 𝑅𝑅 be a relation defined on ℤ𝑍 by 𝑥𝑅𝑦𝑥𝑅𝑦 if and only if 𝑥+𝑦>0𝑥+𝑦>0.

Q1. Let 𝐴 = {0,1,2,3,4,5,6,7} suppose 𝑅 𝑎𝑛𝑑 𝑇 are two relations on 𝐴 such that 𝑅 = {(𝑥, 𝑦): 𝑥 + 2𝑦 ≥ 4}, 𝑇 = {(𝑥, 𝑦): 2𝑥 + 3𝑦 ∈ 𝐴} Write 𝑅, 𝑇, 𝑎𝑛𝑑 𝑅°𝑇

If 𝑓(𝑥) = { 𝑥sin 1 𝑥 , 𝑥 ≠ 0 0, 𝑥 = 0 , then lim𝑥→0𝑓(𝑥) =

If 𝑣=𝑓𝑥,𝑦, define 𝛿𝑣

Define Partial Order relation and check whether R is Partial Order relation.R= {(x,y) 𝑖𝑓 𝑦 = 𝑥𝑟, 𝑟 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑎𝑛𝑑 𝑎, 𝑏 ∈ 𝑍}

We consider the relation 𝑅={(𝑎,𝑎),(𝑎,𝑏),(𝑎,𝑐),(𝑎,𝑑),(𝑎,𝑒),(𝑏,𝑐),(𝑏,𝑒),(𝑑,𝑎),(𝑒,𝑐)}.Is 𝑅 transitive? Justify briefly