Prove each of the following results without using Venn diagrams or membership tables. (Assume a universe U.)
Question:
(a) If A ⊂ B and C ⊂ D, then A ∩ C ⊂ B ∩ D and A ∪ C ⊂ B ∪ D.
(b) A ⊂ B if and only if A ∩ = θ.
(c) A ⊂ B if and only if ∪ B = °U.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 83% (12 reviews)
a x A c x A and x C x B and x D since A B and C D x B D so A C B D x A U C x A o...View the full answer
Answered By
Bhartendu Goyal
Professional, Experienced, and Expert tutor who will provide speedy and to-the-point solutions. I have been teaching students for 5 years now in different subjects and it's truly been one of the most rewarding experiences of my life. I have also done one-to-one tutoring with 100+ students and help them achieve great subject knowledge. I have expertise in computer subjects like C++, C, Java, and Python programming and other computer Science related fields. Many of my student's parents message me that your lessons improved their children's grades and this is the best only thing you want as a tea...
3.00+
2+ Reviews
10+ Question Solved
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Question Posted:
Students also viewed these Linear Algebra questions
-
Prove each of the following statements. a) 2n + 1 < 2n for n = 3, 4,.... b) n < 2n for n = 1, 2,.... c) n2 < 2n + 1 for n = 1, 2,.... d) n3 < 3n for n = 1, 2,....
-
Prove each of the following for any base a and any positive number x. loga (1/x) = -loga x = log1/a x loga (z + (x2 - 5)/5) = -loga (x - x2 - 5)
-
Prove each of the following for any complex numbers z1, z2,........ , zn, where i2 = -1 and z is the conjugate of z. 2 = z"
-
The formula for the power output P of a battery is P = VI - RI where V is the electromotive force in volts, R is the resistance in ohms, and I is the current in amperes. Find the current that...
-
The Willow Café is located in an open-air mall. Its lease expires this year and the restaurant owner has the option of signing a 1-, 2-, 3-, 4-, or 5-year lease. However, the owner is...
-
A lawn care company tried to predict the demand for its service by zip code, using the housing density in the zip code area as a predictor. The owners obtained the number of houses and the geographic...
-
As shown in Fig. P8.71, water "bubbles up" 3 in. above the exit of the vertical pipe attached to three horizontal pipe segments. The total length of the 0.75-in.diameter galvanized iron pipe between...
-
IT auditors need people skills as well as technical skills. One such skill is the ability to interview effectively. Discuss some techniques or tools that might help an interviewer get the best...
-
A glass window is 2.0 m wide and 1.5 m high and 7.5 mm thick. The temperature of the inner surface is 18 C and that of the outer surface is 11 C. (a) Find the rate of heat flow through the window....
-
Consider the following 0x86 program: .data array DWORD 1,2,3,4,5,6,7,8,9 aravSize -(S-array)/4 ; array .code main PROC mov ecx,arraySize-1 mov esi.OFFSET array L1: mov eax. [esi] sda mov bx,2 idiv bx...
-
Determine which of the following statements are true and which are false. (a) Z+ Q+ (b) Z+ Q (c) Q+ R (d) R+ Q (e) Q+ R+ = Q+ (f) Z+ R+ = R (g) R+ C = R+ (h) C R = R (i) Q+ Z = Z
-
Prove or disprove each of the following: (a) For sets A, B, C U, A C = B C A = B. (b) For sets A, B, C U, A U C = B U C A = B. (c) For sets A, B, C U, [(A C = B C) (A U C = B U C)] A = B....
-
Apply the product rule for exponents, if possible. x 3 x 5 x 9
-
To what extent do private portfolio investments in developing countries benefit the recipient countries? What are the potential costs and risks to both investors and recipients? Explain your answer.
-
Which statements about the following code are correct? A. It consistently prints 6. B. It consistently prints 7. C. It consistently prints another value. D. It does not consistently print the same...
-
Which of the following can fill in the blank to have the code print 44? A. Only map B. Only mapToInt C. Only mapToObject. D. Both map and mapToInt E. Both map and mapToObject F. map, mapToInt, and...
-
Economic growth is said to be a necessary but not sufficient condition to eradicate absolute poverty and reduce inequality. What is the reasoning behind this argument?
-
What is the significance of the debt service ratio? Can indebted countries do anything to lower this ratio? Explain your answer.
-
In Exercises find (a) a right end behavior model and (b) a left end behavior model for the function. (x) = In |x| + sin x
-
Don Griffin worked as an accountant at a local accounting firm for five years after graduating from university. Recently, he opened his own accounting practice, which he operates as a corporation....
-
In each of Exercises, classify the function as linear, quadratic, cubic, quartic, rational, exponential, or logarithmic. a. f (x) = 5 - x2 + x4 b. f (x) = 2x c. f (x) = - 3/4 d. f (x) = 4x - 8
-
Express as a single logarithm and, if possible, simplify. a. loga (x2 + xy + y2) + loga (x - y) b. loga (a10 - b10) - loga (a + b)
-
Express as a sum or a difference of logarithms. a. loga (x - y) / (x2 - y2) b. loga (9 - x2)
-
Higgins Company began operations last year. You are a member of the management team investigating expansion ideas that will require borrowing funds from banks. On January 1 , the start of the current...
-
On April 1, 2021, Windsor, Inc. purchased $615,000 of 6% bonds for $639,225 plus accrued interest as an available-for-sale security. Interest is paid on July 1 and January 1 and the bonds mature on...
-
Use the graphical method for linear programming to find the optimal solution for the following problem. Minimize C=3x+15y subject to 2x + 4y 12 5x + 2y 10 and x 0, y 0.
Study smarter with the SolutionInn App