1
answer
0
watching
622
views
12 Nov 2019
Which of the following rules are operations on the indicated set? (z designates the set of the integers the rational numbers, and R the real numbers.) For each rule which is not an operation, explain why not. Example a*b = a + b/ab, on the set z. Solution This is not an operation on z. There are integers a and b such that {a + b)/ab is not an integer. example, 2 + 3/2 middot 3 = 5/6 is not an integer.) Thus, z is not closed under *. a * b = squareroot |ab|, on the set Q. a * b = a ln b, on the set {x elementof R: x > 0}. a * b is a root of the equation x^2 - a^2 b^2 = 0, on the set R. Subtraction, on the set z. Subtraction, on the set {n elementof r. greaterthanorequalto 0}. a * b = |a - b, on the set {n elementof r. greaterthanorequalto 0}.
Which of the following rules are operations on the indicated set? (z designates the set of the integers the rational numbers, and R the real numbers.) For each rule which is not an operation, explain why not. Example a*b = a + b/ab, on the set z. Solution This is not an operation on z. There are integers a and b such that {a + b)/ab is not an integer. example, 2 + 3/2 middot 3 = 5/6 is not an integer.) Thus, z is not closed under *. a * b = squareroot |ab|, on the set Q. a * b = a ln b, on the set {x elementof R: x > 0}. a * b is a root of the equation x^2 - a^2 b^2 = 0, on the set R. Subtraction, on the set z. Subtraction, on the set {n elementof r. greaterthanorequalto 0}. a * b = |a - b, on the set {n elementof r. greaterthanorequalto 0}.
Reid WolffLv2
11 Aug 2019