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

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

Obtain the derivative of 𝑧=(2𝑥-𝑦)(𝑥+3𝑦) with respect to yQuestion 10Answera.5𝑥-6𝑦b.(2𝑥-1)(𝑥+3)c.4𝑥+5𝑦d.(2-𝑦)(1+3𝑦)

If 𝑅(𝑥, 𝑦) = “𝑥 𝑟𝑒𝑙𝑖𝑒𝑠 𝑢𝑝𝑜𝑛 𝑦, ” express the following in unambiguousEnglish:a. ∀𝑥 ∃𝑦 𝑅(𝑥, 𝑦)b. ∀𝑦 ∃𝑥 𝑅(𝑥, 𝑦)c. ∀𝑥 ∀𝑦 𝑅(𝑥, 𝑦)

Is the sentence ∃𝑦∀𝑥𝑆(𝑥,𝑦)∃𝑦∀𝑥𝑆(𝑥,𝑦) true under the interpretation where 𝑥𝑥 and 𝑦𝑦 range over the integers and 𝑆(𝑥,𝑦)𝑆(𝑥,𝑦) is "𝑦<(𝑥+2)2𝑦<(𝑥+2)2"?

Solve the system of equations.2𝑥+3𝑦=8−2𝑦=−4Group of answer choices(1,2)(−1,−2)(−1,2)(1,−2)