43. Show that if A is a subset of a universal set U, then a) A Ⓡ A = Ø. c) AU=A. b) A Ø = A. d) A @Ā = U.

Q: Consider the following sets. A = {1,3,5,7,9} B = {3,6,9} C = {2,4,6,8} Find each of the following:…

A:

Q: Does every set A have an inverse? What is it? d) Is (U, A) a group?

A: c) Let A∈U. To find the inverse of A. For, let us find the identity element first. A△∅=A-∅∪∅-A=A∪∅=A…

Q: a) Suppose A is a finite set and B is any set. Show that |A| = |A\ B| + |A n B|. (Hint: Use Theorem…

A:

Q: Let U = {all sports}: A= { all outdoor sports } ; B= { all sports using a ball } ; C= { all water…

A: Consider the given information:

Q: Let A= {2, 3, 4}, B= {3, 4, 5, 6}, and suppose the universal set is U= {1, 2, 3, .., 9} List all the…

A: Universal Set: We consider all the sets to be the subsets of a given fixed set known as universal…

Q: = U.

A:

Q: Let U = {t,u,v,w,x,y,z), A = {u,w}, D = {x,y), C = {u,v,w), B = {u,v,w,x,z). Tell whether the…

A: Given: Let U={t,u,v,w,x,y,z}, A={u,w}, D={x,y}, C={u,v,w}, B={u,v,w,x,z}. U is the universal set.

Q: Consider the following sets. A = {1,3,5,7,9} B = {3,6,9} C = {2,4,6,8} Find each of the following:…

A:

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: 7. Determine whether each of these pairs of sets are equal. a) {1, 3, 3, 3, 5, 5, 5, 5, 5)}, {5, 3,…

A: 7. (a) Let the given sets are A= { 1,3,3,3,5,5,5,5,5 } and B= { 5,3,1 } = { 1,3,5 } We know that a…

Q: Given a universal set U and sets A, B CU, prove that A C Bº if and only if AnB = 0. Prove that (AN…

A:

Q: 1. List the elements of each set where N= {1,2,3...} a.) A = EN|3 < x < 9} %3D b.) B = x€ N|x is…

A:

Q: Let A and B be two sets. a) Suppose that A and B are both countably infinite sets. Prove that there…

A:

Q: Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}.  a) A union B b) A intersection B c) The complement of…

A:

Q: Consider the sets: A= {red, green, blue} C= {red, orange, yellow, green, blue, purple) a) Find A U B…

A:

Q: Exercise: Find the cardinal number of each set a) K = {2,4,8,16} c) R={4,5..,12,13} b) M = {0} d) Ø…

A:

Q: The set ZUZU {0} is equal to: a) 이이이이이 b) NRQNN None of these. 3. True or false? For any set A, ØCA.…

A:

Q: For A= {2,x,y} B= {w,x} C={1,2,3} U={1,2,3,4,w,x,y,z} Use proper set notation a) C- A AUB c) d) e)…

A:

Q: 6. Let U be a set and let X be the power set of U (that is, the set of all subsets of U). Consider…

A:

Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: 28 Let A, B and C be subsets of a universal set U with CCANB. Suppose n(U) = 50, n(A) = n(B) = 25,…

A: Option f) is correct. Answer =7

Q: 23. Find the power set of each of these sets, where a and b are distinct elements. a) {a} b) {a, b}…

A: