The zero product property says that if a product of two real numbers is 0, then one of the numbers must be 0. (a) Which of the following expresses the zero product property formally using quantifiers and variables? O v real numbers x and y, if x = 0 and y = 0 then xy = 0. Ov real numbers x and y, if xy = 0 then x = 0 and y = 0. O v real numbers x and y, if xy = 0 then x = 0 or y = 0. O v real numbers x and y, if x = 0 or y = 0 then xy = 0. (b) Which of the following is the contrapositive of the zero product property? O v real numbers x and y, if xy # 0 then x # 0 or y # 0. O v real numbers x and y, if xy + 0 then x # 0 and y # 0. O v real numbers x and y, if x # 0 or y 0 then xy # 0. O v real numbers x and y, if x # 0 and y # 0 then xy # 0. (c) Which of the following is an informal version (without quantifier symbols or variables) for the contrapositive of the zero product property? O For any two real numbers, if at least one of them is nonzero then their product is nonzero. O If the product of two real numbers is nonzero, then both numbers are nonzero. O If the product of two real numbers is nonzero, then neither number is zero. O If neither of two real numbers is zero, then their product is nonzero.
The zero product property says that if a product of two real numbers is 0, then one of the numbers must be 0. (a) Which of the following expresses the zero product property formally using quantifiers and variables? O v real numbers x and y, if x = 0 and y = 0 then xy = 0. Ov real numbers x and y, if xy = 0 then x = 0 and y = 0. O v real numbers x and y, if xy = 0 then x = 0 or y = 0. O v real numbers x and y, if x = 0 or y = 0 then xy = 0. (b) Which of the following is the contrapositive of the zero product property? O v real numbers x and y, if xy # 0 then x # 0 or y # 0. O v real numbers x and y, if xy + 0 then x # 0 and y # 0. O v real numbers x and y, if x # 0 or y 0 then xy # 0. O v real numbers x and y, if x # 0 and y # 0 then xy # 0. (c) Which of the following is an informal version (without quantifier symbols or variables) for the contrapositive of the zero product property? O For any two real numbers, if at least one of them is nonzero then their product is nonzero. O If the product of two real numbers is nonzero, then both numbers are nonzero. O If the product of two real numbers is nonzero, then neither number is zero. O If neither of two real numbers is zero, then their product is nonzero.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:The zero product property says that if a product of two real numbers is 0, then one of the numbers must be 0.
(a) Which of the following expresses the zero product property formally using quantifiers and variables?
O v real numbers x and y, if x = 0 and y = 0 then xy = 0.
O v real numbers x and y, if xy = 0 then x = 0 and y = 0.
O v real numbers x and y, if xy = 0 then x = 0 or y = 0.
O v real numbers x and y, if x = 0 or y = 0 then xy = 0.
(b) Which of the following is the contrapositive of the zero product property?
O v real numbers x and y, if xy + 0 then x + 0 or y # 0.
O v real numbers x and y, if xy + 0 then x # 0 and y # 0.
O v real numbers x and y, if x # 0 or y = 0 then xy # 0.
O v real numbers x and y, if x # 0 and y # 0 then xy # 0.
(c) Which of the following is an informal version (without quantifier symbols or variables) for the contrapositive of the zero product property?
O For any two real numbers, if at least one of them is nonzero then their product is nonzero.
O If the product of two real numbers is nonzero, then both numbers are nonzero.
O If the product of two real numbers is nonzero, then neither number is zero.
O If neither of two real numbers is zero, then their product is nonzero.
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