MHB How to Justify Each Step Using Commutativity and Associativity?

  • Thread starter Thread starter happyprimate
  • Start date Start date
AI Thread Summary
The discussion focuses on verifying the expression (a-b)+(c-d) = (a+c)+(-b-d) using the properties of associativity and commutativity. The user demonstrates each step of the transformation, applying associativity to regroup terms and commutativity to rearrange them. The final expression confirms that the original and transformed equations are equivalent. The verification process emphasizes the importance of these mathematical properties in simplifying expressions. Overall, the approach effectively illustrates how to justify each step in the equation.
happyprimate
Messages
7
Reaction score
2
Exercise 3 Chapter 1 Basic Mathematics Serge Lang

Verifying my answer.

My answer:

(a-b)+(c-d) = (a+c)+(-b-d)

Let p = (a-b)+(c-d) We need to show that p = (a+c)+(-b-d)

(a-b)+(c-d)

a+(-b+(c-d)) Associativity

a+((-b+c)-d) Associativity

a+((c-b)-d) Commutativity

((a+c)-b)-d) Associativity

(a+c)+(-b-d) Associativity
 
Mathematics news on Phys.org
Looks good to me.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

Similar threads

Back
Top