Let A, B and C be sets. Prove that Ax (B-C) = (A x B) - (AXC).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help solving those discreete math problems.
![Problem 2
Let A, B and C be sets. Prove that Ax (B-C) = (A x B) – (A × C).
Problem 3
Let A and B be sets. The symmetric difference of A and B, denoted AAB, is the set
AAB = (A - B) U (B - A). Prove: AAB = (AUB) - (ANB).
Problem 4
Let A and B be sets. The power set of A, denoted P(A), is the set defined by: P(A) =
{X X CA}. Prove or give a counterexample.
(i) P(AUB) = P(A)UP(B)
(ii) P(ANB) = P(A)nP(B)
Problem 5
Let A be a set. If A has relements, how many elements are there in: P(A), P(P(A)),
P(A) × P(A), P(A × A), and P(A × A) × P(A × A)?
Problem 6
Calculate U-1An and no1 An where for each n EN the set An is defined as:
(i) An = {0, 1, 2, 3, , 2n}
(ii) An = {TER|x>n}
(iii) A₂ = {x € R | < x < √√² + 1}
(iv) An = {x ER |-n<x</}
(v) An = { x = Q | √√/2 - 1/2 ≤ x ≤ √√2 + ¹}
(vi) An = {n-1, n, n + 1}
(vii) An = [-1,3+ ]U[5, 5n+
n
n
(viii) An = (-, 1] U (2,
n
3n - 1,
=
n
7n+1
(ix) A‚ = [0, n +¹]u[7, 7n +¹)
An
n+2
n
3 5n+2.
(x) An = (2, 5m + ²) u {10+ n}
U
n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe742bcfc-6571-4eb6-8020-0d244ddd1492%2F213d58f5-6e58-42bb-b5f2-aa2370da6c5c%2Fv9lt78o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 2
Let A, B and C be sets. Prove that Ax (B-C) = (A x B) – (A × C).
Problem 3
Let A and B be sets. The symmetric difference of A and B, denoted AAB, is the set
AAB = (A - B) U (B - A). Prove: AAB = (AUB) - (ANB).
Problem 4
Let A and B be sets. The power set of A, denoted P(A), is the set defined by: P(A) =
{X X CA}. Prove or give a counterexample.
(i) P(AUB) = P(A)UP(B)
(ii) P(ANB) = P(A)nP(B)
Problem 5
Let A be a set. If A has relements, how many elements are there in: P(A), P(P(A)),
P(A) × P(A), P(A × A), and P(A × A) × P(A × A)?
Problem 6
Calculate U-1An and no1 An where for each n EN the set An is defined as:
(i) An = {0, 1, 2, 3, , 2n}
(ii) An = {TER|x>n}
(iii) A₂ = {x € R | < x < √√² + 1}
(iv) An = {x ER |-n<x</}
(v) An = { x = Q | √√/2 - 1/2 ≤ x ≤ √√2 + ¹}
(vi) An = {n-1, n, n + 1}
(vii) An = [-1,3+ ]U[5, 5n+
n
n
(viii) An = (-, 1] U (2,
n
3n - 1,
=
n
7n+1
(ix) A‚ = [0, n +¹]u[7, 7n +¹)
An
n+2
n
3 5n+2.
(x) An = (2, 5m + ²) u {10+ n}
U
n
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