The set D1 consists of three students: Garth, who is 5 feet 11 inches tall; Erin, who is 5 feet 6 inches tall; and Marts, who is 6 feet tall. The set D2 consists of four students: Dale, who is 6 feet tall; Garth, who is 5 feet II inches tall; Erin, who is 5 feet 6 inches tall; and Marty, who is 6 feet tall. The set D3 consists of one student: Dale, who is 6 feet tall. The set D4 consists of three students: Pat, Sandy, and Gale, each of whom is 5 feet 11 inches tall.
T2(x, y) is the propositional function “x is taller than or the same height as y.”
Write the negation of each proposition in Exercises 1-4 in words and symbolically.
Exercise 1
The set D1 consists of three students: Garth, who is 5 feet 11 inches tall; Erin, who is 5 feet 6 inches tall; and Marts, who is 6 feet tall. The set D2 consists of four students: Dale, who is 6 feet tall; Garth, who is 5 feet II inches tall; Erin, who is 5 feet 6 inches tall; and Marty, who is 6 feet tall. The set D3 consists of one student: Dale, who is 6 feet tall. The set D4 consists of three students: Pat, Sandy, and Gale, each of whom is 5 feet 11 inches tall.
T2(x, y) is the propositional function “x is taller than or the same height as y.” Write each proposition in words.
∀x∀y T2(x, y)
Exercise 2
The set D1 consists of three students: Garth, who is 5 feet 11 inches tall; Erin, who is 5 feet 6 inches tall; and Marts, who is 6 feet tall. The set D2 consists of four students: Dale, who is 6 feet tall; Garth, who is 5 feet II inches tall; Erin, who is 5 feet 6 inches tall; and Marty, who is 6 feet tall. The set D3 consists of one student: Dale, who is 6 feet tall. The set D4 consists of three students: Pat, Sandy, and Gale, each of whom is 5 feet 11 inches tall.
T2(x, y) is the propositional function “x is taller than or the same height as y.” Write each proposition in words.
∀xƎy T2(x, y)
Exercise 3
The set D1 consists of three students: Garth, who is 5 feet 11 inches tall; Erin, who is 5 feet 6 inches tall; and Marts, who is 6 feet tall. The set D2 consists of four students: Dale, who is 6 feet tall; Garth, who is 5 feet II inches tall; Erin, who is 5 feet 6 inches tall; and Marty, who is 6 feet tall. The set D3 consists of one student: Dale, who is 6 feet tall. The set D4 consists of three students: Pat, Sandy, and Gale, each of whom is 5 feet 11 inches tall.
T2(x, y) is the propositional function “x is taller than or the same height as y.” Write each proposition in words.
Ǝx∀y T2(x, y)
Exercise 4
The set D1 consists of three students: Garth, who is 5 feet 11 inches tall; Erin, who is 5 feet 6 inches tall; and Marts, who is 6 feet tall. The set D2 consists of four students: Dale, who is 6 feet tall; Garth, who is 5 feet II inches tall; Erin, who is 5 feet 6 inches tall; and Marty, who is 6 feet tall. The set D3 consists of one student: Dale, who is 6 feet tall. The set D4 consists of three students: Pat, Sandy, and Gale, each of whom is 5 feet 11 inches tall.
T2(x, y) is the propositional function “x is taller than or the same height as y.” Write each proposition in words.
ƎxƎy T2(x, y)
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