Question: Prove that if a; b R, then (a) -(a + b) = (-a) + (-b), (b) (-a) (-b) = a b, (c)

Prove that if a; b ∈ R, then
(a) -(a + b) = (-a) + (-b),
(b) (-a) ∙ (-b) = a ∙ b,
(c) 1/(-a) = -(1/a),
(d) -(a/b) = (-a)/b if b ≠ 0.

Step by Step Solution

★★★★★

3.40 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a a b 1a b 1a 1 b a ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

829-C-I (919).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Prove that if a

Q:

Use the Reflection Principle and analogous results about suprema to prove the following results. a) [APPROXIMATION PROPERTY FOR INFIMA] Prove that if a set E R has a finite infimum and > 0 is any...

Q:

(a) Prove that if A is symmetric and tridiagonal, then all matrices Ak appearing in the Q R algorithm are also symmetric and tridiagonal. First prove symmetry. (b) Is the result true if A is not...

Q:

Provide solutions.to the following attachments. Suppose that the business oyole in the United States is best described by R30 theory and that a new technology increases productivity. Show the effect...

Q:

Answer.the following attachments. 1.Exchange Rate Overshooting Use the foreign exchange and money market diagrams to answer the following questions about the relationship between the Indian rupee...

Q:

Question 1 (5 points) Identify the statement given below. Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles...

Q:

2. [5 pts] Consider the function : R \ 0 R, 9 (x) = x+ (a) [1 pt] Draw the graph of f. (b) [2 pts] Let A = [3,0], B = (0,). Prove that f(x) : A B is injective by two different methods i. [1 pt] Using...

Q:

For each relation given below determine whether it is reflexive, irreflexive or neither; symmetric, asymmetric, antisymmetric, or none of the above; transitive or not. Rom this determine whether it...

Q:

Let r follows the process drt = (r - rt)dt + dXt Use Ito's Lemma to compute the law of motion of P = F(r), for F(X) given by (a) F(r) = A + B r where A, B are two constants. (b) F(r) = e A-B r where...

Q:

If a; b R and b 0, show that: (a) |a| = a2; (b) |a/b| = |a|/|b|.

Q:

Teck Lock Corp. is considering replacing an old drill press with a new model. The following data is available: Old Machine New Machine Price $300,000 $600,000 Accumulated Depreciation 90,000 -0-...

Q:

In a counter-current flow heat exchanger, temperature difference between hot and cold fluid at all positions is held constant. If effectiveness of the heat exchanger is 0.65 and heat capacity ratio...

Q:

Based on file mentioned in your course representation in week 1 8 , modify the Matlab code to find the parameters based on below circuit Please send me the code and result as report.

Q:

Maria purchased a Louis Vuitton purse for her mom because of the dust cover that protects the purse from wear and tear. This is an example of packaging used as a marketing tool for ________. a. brand...

Q:

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five...

Q:

Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about...

Q:

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = sin2 x, y = 0, 0

Q:

THIS IS NOT THE ANSWER : Basic EPS: $0.68 Diluted EPS: $0.58 On December 31, 2023, Chi Chow Company had outstanding 420,000 shares of common stock and 42,000 shares of 8% cumulative preferred stock...

Q:

Perteet Corporation's relevant range of activity is 7,500 units to 14,500 units. When it produces and sells 11,000 units, its average costs per unit are as follows: Average Cost per Unit Direct...

Q:

Required information [The following information applies to the questions displayed below.] On January 1, 2024, Splash City issues $430,000 of 8% bonds, due in 15 years, with interest payable...