
do 4,5,6
Let A = {1,2,3) and B = {a,b). 1. Is the ordered pair (3.a) in the Cartesian product Ax B? Explain. 2. Is the ordered pair (3.a) in the Cartesian product A x A? Explain. 3. Is the ordered pair (3, 1) in the Cartesian product A x A? Explain. 4. Use the roster method to specify all the elements of Ax B. (Remember that the elements of Ax B will be ordered pairs. =1'. 5. Use the...
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.
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'
List the elements of the following setswhere P = {1,2,3...}A={x:x € P, 3 < x < 12}B={x:x € P, x is even, x < 15}C={x:x € P, 4 + x € 3}D={x:x € P, x is multiple of 5}
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...
Prove or disprove: for all sets A, B, C and D, (Ax B) U (Cx D) (AUC) x (BUD).
A. = 6 B. =9. C. =69
5) Obtain a, b, c and d if (c-2 c+d 2a -b 3a Sat-d) = ( 28) BUM2225 Show that (A + B) = BT AT where A= =(CA 0 -В. and B = ( A) -B 7) y2 If A = xy 1 = ( Obtain A2 -x2 -xy 8) 11 S=CA -), find s- 9) If f(x) = Ax-B, g(x) = Cx2 + B, find (a) (f + g)(2) (b) (g-(-3)...
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...
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
Problem 11.16. Let X = {XE Ζ+ : x-100): that is, X is the set of all integers from l to 100. For each Y E 9(X) we define AY (2 E 9(X) : Y and Z have the same number of elements) (a) Prove that AY : Y є 9(X)} partitions 9(X). (b) Letdenote the equivalence relation on (X) that is associated with this partition (according to Theorem 11.4). If possible, find A, B, and C such that 1....