Let U={1,2,3,4,5,6} A={1,2,3} B={1,3,5} C={5,6} List the elements of the following sets. (a) (A union B)', (b) A intersection B intersection C, (c) A'intersection B intersection C (d) A'intersection C'
Question 5,12,14,15,16 Exercises for Section 1.4 A. Write the following sets by listing their elements between braces. 1. 9({{a,b}, {c}}) 7. 9({a,b}) x P ({0,1}) 2. P{{1,2,3,4}) 8. P{{1,2} + {3}) 3. 9({{0},5}) 9. P{{a,b} Ⓡ {0}) 4. P({RQ}) 10. {X€ 9 ({1,2,3}): \X]s 1} 5. 9(9({2})) 11. {XC9(1,2,3}): [X|S 1} 6. 9({1,2}) * F ({3}) 12. {X € F ({1,2,3}):2 €X} B. Suppose that |A| = m and \B= n. Find the following cardinalities. 13. [PPP(A))) 17. |{X €...
Consider the poset S = ({P{1,2,3} - {0}), S) (a) List any minimal elements (b) If it exists give the minimum element (c) List any maximal elements (d) If it exists give the maximum element (e) Give the Hasse diagram for S
5-13 please Homework on sets 1. let the universe be the set U (1,23. .,1.0), A (147,10), B- (1,2 list the elements for the following sets. a. B'nt C-A) b. B-A c. ΒΔΑ 2. Show that A (3,2,1] and B (1,2,3) are equal 3. Show that X Ixe Rand x > 0 and x < 3j and ( 1,2) are equal. 5. Use a Ven diagram and shade the given set. (cnA)-(B-Arnc) Show that A (x| x3-2x2-x+2 O) is not...
2. If A = {a, b, c), B = { 1,2,3), c = {x), and D-9, list all of the elements in each of the following sets. (a) A x B (d) Ax D
Problem 2. For the following statements, write down whether true or false (No justification needed, and for ease of grading, please make it clear what is) (1) (a) xE (b) х€ {{x}} (c) x}€{{x}} (d) } E (2) (a) C 1,2,3 (b) E {1,2,3 (c)E P({1,2,3} (d) n0 (3) (a) 1,2,3 (b) {1,2,3} с {1, 2, 3} (c) An0 (d) AU A (4) a) ZnZ = Z (b) ZUZ 22 your answer Problem 3. List the elements of the following...
cept of a randon PROBLEMS 1.1-1. Specify the following sets by the rule method. A= (1,2,3), B = (8, 10, 12. 14), C (1, 3, 5, 7,... 1.1-2. Use the tabular method to specify a class of sets for the sets of Problem 1.1-1. uncountable, or finite or infinite. A (1), B= (x= 1}, C ={0 < integers), D = (children in public school No. 5), E={girls in public school No. 5), F = {girls in class in public 1.1-3....
Q1 Ifs [0, 1,2,3, 4, 5,6,7,8,9) and A f0,2,4,6,8, B - (1,3,5,7,9), C (2,3,4,5), and D 11,6,7), list the elements of the sets corresponding to the following events: (a) A U C, (b) AnB; (d) (C' n D)UB (e) (s n cy'; (f) AnCn D.
Problem 9 Consider the directed network on vertices V s, 1,2,3, 4,5,t) given by the following list. An element of this list has the forn (í,j,c) where (i,j) is an are of the network, and c is the capacity of are (i.j) (3, 4,2), (3,,15), (3, 5,11), (3, t, 12, (4,5,9), (4, t, 15), (5,t,7) ·What is the maximuln 8 → t flow in this network? (You may use AMPL to compute this.) What is a minimum cut? EXTRA CREDIT;...
#4 ,0, C, d, e, f,g, h}. (a) Using these elements, construct two sets A and B satisfying | A=5, |B| = 4 and |An Bl 2 (b) Using the sets you chose, compute An B| 4. Let A {r : -1 < x < 1}, B = {x : -2 < x < 2}and C = {x : -2 < x < 3}, where xER. Determine whether the following statements are true or false. (a) AC B (b) C...