5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a) X-Y is open. (b) Y-X is closed.

Q: 12] and a3 = -20 4 -------- Let a₁ = h 5 2 The set {a1, a2, a3} will span R³ unless h = 0

A:

Q: 13. Let X and Y be subsets of any finite, nonempty set. Give the properties of the relation where X…

A:

Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: to,' i.e. Let X be the space of integers and let R be relation 'less than or equal x Ry if x ≤ y…

A: The given relation is .

Q: Prove that for any set relation R (we did not pick it to be "on" any particular set) R* =N{Q:RC Q^ Q…

A: Given that any set relation R.

Q: I have the following question and I also have the answer, I just dont understand why and how this…

A:

Q: Dijec not need to prove you function is a bijection): (a) N and Z (b) Rand (1, ∞) (c) (0, 2) and (3,…

A:

Q: 11. Let A(3, 4, 5) and B=(4,5,6) and let S be the "divides" relation. That is, for all (x, y) e Ax…

A:

Q: We defined the relation between sets by A ~ B means that there there is a 1-1 correspondence ƒ : A →…

A: We define the relation ~ between sets by A~B means that there is a one-one correspondence f:A→B Show…

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: Consider the family of sets F = {Ap}peP, where P denotes the set of prime numbers, and Ap= {p" |…

A:

Q: Let ∅ be the empty set. Let X be the real line, the entire plane, or, in the three-dimensional case,…

A: Given:

Q: 1) Let the set S be defined as S = {x | x is a U.S. President} Find n(S). 2) Define compliment to a…

A: use the basic property of sets .

Q: F and Hare sets of real numbers defined as follows. F = {ww≤ 4} H = {w|w>5} Write FUH and FnH using…

A: We can find the union and intersection of sets in the below steps.

Q: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

A:

Q: Suppose that you have two sets, and you know that both sets are convex. Proven that the intersection…

A: convex set is a set of points such that, given any two points x,y in that set, the straight line…

Q: TOVE 4.55. Let A, B and C be sets. Prove that (A-B) (A-C)=A-(BUC).

A:

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: SETS Prove that X ⊆ Y if and only if X ∪ Y = Y.

A: Draw a sets of X and Y and plot different cases and check all conditions having XUY=Y.

Q: Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - U B, = N(A – B„,).…

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: Prove that the relation ∼ between sets is symmetric and transitive.

A:

Q: X, Y and Z be subsets of the set . Verify the following properties: XCY XUY=Y⇒XnY=X -UI 3)

A:

Q: A = {y EZ:2 < y ≤ 9 and y is odd}. B = {1, 4, 6} C = {yEZ: y ≤ 10 and y is even}. D = {y EZ: y ≤ 7…

A:

Q: Let P(x) = x¹ + (2 − i)x³ + (1 − 2i)x² + (2 − i)x − 2i. Find all real values of a such that when the…

A:

Q: Topology:Q13 or 14 For each of the following, if the statement about a topological space is always…

A: Solution (13):-" the interior of the closure of a set equal to the interior of that set"    The…

Q: et the domain be the set of all people. Let: P(x, y): x knows y. Vhich of the following is the…

A: Here we use predicate logic

Q: (b) Let={A i EN} be a family of sets with A₁ CA₂ CCA10 C... Prove that nA = A₁.

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.