SECTION 1.5 Nested Quantifiers 1. (2x6 = 12 points) Translate these statements into English, where the domain for each variable consists of all real numbers. Determine the truth values of each statement. a) Ex Vy (x + 2y = y) b) VxVy (((-2 0)) c) 3x3y (xy + x + xy + 1)) d) Vx3y (3x + y = y + 1) e) VxWya: (xy = y --) f) Vx3y3: (x + y = xz + y) 2. (2*8 = 16 points) Let F(x, y) be the statement "x is following y on twitter, and S(x) be the statement "x is a student at UH, where the domain for x consists of all people. Express each of these statements by a simple English sentence. a) 3x F(x, Alan Turing) b) VxVy F(x, y) c) Vxy F(x, y) d) Byx F(x, y) e) 3x Vy F(x, y) f) Zyx (Sy) F(x, y)) g) 3xVy (S(x) ^-F(x, y)) h) Vxy (S(x)+F(x, y) SECTION 1.5 Nested Quantifiers 1. (2x6 = 12 points) Translate these statements into English, where the domain for each variable consists of all real numbers. Determine the truth values of each statement. a) Ex Vy (x + 2y = y) b) VxVy (((-2 0)) c) 3x3y (xy + x + xy + 1)) d) Vx3y (3x + y = y + 1) e) VxWya: (xy = y --) f) Vx3y3: (x + y = xz + y) 2. (2*8 = 16 points) Let F(x, y) be the statement "x is following y on twitter, and S(x) be the statement "x is a student at UH, where the domain for x consists of all people. Express each of these statements by a simple English sentence. a) 3x F(x, Alan Turing) b) VxVy F(x, y) c) Vxy F(x, y) d) Byx F(x, y) e) 3x Vy F(x, y) f) Zyx (Sy) F(x, y)) g) 3xVy (S(x) ^-F(x, y)) h) Vxy (S(x)+F(x, y)