Determine the truth value of each of the following statements. We assume that the domain for all variables consists of all real numbers. 1. x y (x 2 = y) 2. x y (x = y 2 ) 3. x y (xy = 0) 4. x...

Determine the truth value of each of the following statements. We assume that the
domain for all variables consists of all real numbers.
1. x y (x
2
 = y)
2. x y (x = y
2
 )
3. x y (xy = 0)
4. x y (x + y  y + x)
5. x (x  0  y (xy = 1))
6. x y (y  0  xy = 1)
7. x y (x + y = 1)
8. x y (x + 2y = 2  2x + 4y = 5)
9. x y (x + y = 2  2x - y = 1)
10. x y z (z = (x + y)/2)

Extracted text: Problem 4: Determine the truth value of each of the following statements. We assume that the domain for all variables consists of all real numbers. 1. Vx 3y (x² = y) 2. Vx 3y (x = y² ) 3. 3x Vy (xy = 0) 4. 3x 3y (x + y # y+x) 5. Vx (x ± 0 → 3y (xy = 1)) 6. Эх Vy (у#0 > ху%3D1) 7. Vx 3y (x + y= 1) 8. 3x 3y (x + 2y =2 ^ 2x + 4y = 5) 9. Vx 3y (x + y =2 ^ 2x - y = 1) 10. Vx Vy 3z (z = (x + y)/2)