Theorem M1: If x is a number, y is a nonzero number, and xy=y, then x=1. Theorem
ID: 1947274 • Letter: T
Question
Theorem M1: If x is a number, y is a nonzero number, and xy=y, then x=1.Theorem M2: If x is a nonzero number, y is a number, and xy=1, then y=(/x)
Theorem M3: If each of x, y, and z is a number, y?0, and yz=x, then z=x(/y)
Theorem M4: If x is a nonzero number, then /(/x)=x
Theorem M5: /1=1
Usable Axioms (use necessary axioms to prove theorems above):
Axiom A1: A list of numbers may be added in any order, with any grouping, without changing the resulting sum.
Axiom A2: There is a number called zero, denoted by 0, such that if 'a' is a number then 'a'+0='a'.
Axiom A3: If 'a' is a number then -'a'(read minus a) is a number and 'a'+(-a)=0.
Axiom M1: A list of numbers may be multiplied in any order, with any grouping, without changing the resulting product.
Axiom M2: There is a number called one, denoted by 1, such that if 'a' is a number, then 1a=a
Axiom M3: If 'a' is a nonzero number, then /a (read slash 'a') is a number and 'a'(/a)=1
Axiom D: If each of x, y, and z is a number then x(y+z)=xy+xz
Axiom NE: 0 does not equal 1
Explanation / Answer
Theorem M1: If x is a number, y is a nonzero number, and xy=y, then x=1. As xy = y, cancelling y, so x = 1 Theorem M2: If x is a nonzero number, y is a number, and xy=1, then y=(/x) xy = 1, dividing both sides by y x = 1/y Theorem M3: If each of x, y, and z is a number, y?0, and yz=x, then z=x(/y) dividing both sides by y- z = x/y Theorem M4: If x is a nonzero number, then /(/x)=x 1/(1/x) = x Theorem M5: /1=1
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