Problem 1: Let Q(x, y) denote the statement "x has sent an e-mail message to y", where the domain for both x and y consists of all students in your class. Express each of the following quantifications...

Extracted text: Problem 1: Let Q(x, y) denote the statement "x has sent an e-mail message to y", where the domain for both x and y consists of all students in your class. Express each of the following quantifications in English. 1. 3x 3y Q(x, y) 2. 3x Vy Q(x, y) 3. Vx 3y Q(x, y) 4. 3y Vx Q(x, y) 5. Vy 3x Q(x, y) 6. Vx Vy Q(x, y)


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 (x = 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. 3x Vy (y + 0 → xy = 1) 7. Vx 3y (x + y = 1) 8. Ex ay (x + 2y = 2 ^ 2x + 4y = 5) 9. Vx 3y (x + y= 2 ^ 2x - y = 1) 10. Vx Vy 3z (z = (x+y)/2)