The set D1 consists of three students: Garth who is 5 feet 11 inches tall; Erin,
ID: 3749703 • Letter: T
Question
The set D1 consists of three students: Garth who is 5 feet 11 inches tall; Erin, who is 5 feet 6 inches tall; and Marty who is 6 feet tall. The set D2 consists of four students: Dale who is 6 feet tall; Garth, who is 5 feet 11 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 6ft tall. The set D4 consists of three students: Pat, Sandy, and Gale, each of whom is 5 feet 11 inches tall. T2 is the propositional function "x is taller than or the same height as y. Write the following proposition in words x y (x,y)T2(x,y)
Explanation / Answer
The proposition x y (x,y)T2(x,y) can be expressed as:
"There exists atleat one x such that for every y, x is taller than or the same height as y."
Let us consider the sets:
D1 = {Garth: 5 ft 11 inches, Erin: 5ft 6 inches, Marty: 6ft}
D2 = {Dale: 6 ft, Garth: 5 ft 11 inches, Erin: 5ft 6 inches, Marty: 6ft}
D3 = {Dale: 6 ft}
D4 = {Pat: 5 ft 11 inches, Sandy: 5 ft 11 inches, Gale: 5 ft 11 inches}
Considering these sets, we can observe that sets D1 and D2 satify this proposition since "Marty" from set D1 is taller than every student from set D4.
Similarly, sets D1 and D4 atify this proposition since "Marty" from set D1 is taller than every student from set D2.
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