Question

The following is a 3-step proof. Complete the proof.

Given: 1=2
AP=BP
Prove: APD BP
a) APD=BP
b) AP + BP = 1
c) AP = 1/2, BP = 1/2
d) AP - BP = 0

Answer 1

The proof concerns the understanding of equality and the commutative property of numbers. It concludes that if AP equals BP, then both must be half of 1, and their difference is 0.

Step-by-step explanation:

The question appears to be a mathematical proof concerning the properties of equality and operations on numbers. Below is a 3-step proof based on the given information:

1. APD = BP: Since AP = BP, by substitution, APD must also equal BP.
2. AP + BP = 1: Taking the given that 1 = 2, and AP = BP, then AP + BP must equal 1 because AP and BP are both equivalent to half of 1. This respects the commutative property of addition; A + B = B + A.
3. AP = 1/2, BP = 1/2: Since we have established AP + BP = 1, and AP = BP, dividing both sides of the equation by 2 gives us AP = 1/2 and BP = 1/2.
4. AP - BP = 0: Given that AP = BP, subtracting them would yield zero, as any number minus itself is zero.

Additionally, the information on the dependence of events A and B in probability and examples showing division and multiplication of fractions provides context on the equality and basic arithmetic operations used in this proof.