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"?

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"?

Suppose there are integers 𝑎𝑎, 𝑏𝑏, 𝑥𝑥 and 𝑦𝑦 such that 𝑎𝑥+𝑏𝑦=5𝑎𝑥+𝑏𝑦=5, and 55 does not divide 𝑥𝑥. What is gcd(𝑥,𝑦)gcd(𝑥,𝑦)?

Describe the range of the following absolute value function:𝑓(𝑥)=|𝑥+3|−5𝑓(𝑥)=|𝑥+3|−5The range is: 𝑦𝑦 Answer 1 Question 8 Answer 2 Question 8

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=

Show that the following system of equations has unique solutions. Find its solution by thereduction method𝑥 + 𝑦 + 𝑧 = 2, 𝑥 − 2𝑦 + 𝑧 = 8, 3𝑥 + 𝑦 + 𝑧 = 4