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)

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)

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 x,y,z∈R, x+y+z=5, x2+y2+z2=9𝑥,𝑦,𝑧∈𝑅, 𝑥+𝑦+𝑧=5, 𝑥2+𝑦2+𝑧2=9, then length of interval in which x𝑥 lies is

The graph of 𝑦=−|𝑥|𝑦=−|𝑥| is a reflection in the Answer 1 Question 10 of the graph of 𝑦=|𝑥|𝑦=|𝑥|.

Use the formula 𝑦=(𝑥-3)2+3 to find 𝑦 when:𝑎. 𝑥=-2 , 𝑦=  𝑏. 𝑥=-1 , 𝑦=  𝑐. 𝑥=1 , 𝑦=  𝑑. 𝑥=2 , 𝑦=