For all sets A, B,C.Then: (AUB) – (C – A) = AU(B The following algebraic proof is almost finished. You must provide a reason for every step that exactly justifies what was done in the step. (Fill the number into the box) As a reminder the 12 rules are: 1. Commutative Law 2. Associative Law 3. Distributive Law 4. Identity Law 5. Complement Law 6. Double Complement Law 7. Idempotent Law 8. Universal Bound Law 9. De Morgan's Law 10. Absorption Law 11. Complements of U and Empty Set 12. Set Difference Law Proof: Let A, B,C be any sets. Then: by LHS = (AUB) - (C – A) = (AU B) - (CN A°) by = (AUB)n (CN A^)° by = (AU B) N (C° U(A°)*) by = (AU B)n (CUA)

For all sets A, B,C.Then: (AUB) – (C – A) = AU(B The following algebraic proof is almost finished. You must provide a reason for every step that exactly justifies what was done in the step. (Fill the number into the box) As a reminder the 12 rules are: 1. Commutative Law 2. Associative Law 3. Distributive Law 4. Identity Law 5. Complement Law 6. Double Complement Law 7. Idempotent Law 8. Universal Bound Law 9. De Morgan's Law 10. Absorption Law 11. Complements of U and Empty Set 12. Set Difference Law Proof: Let A, B,C be any sets. Then: by LHS = (AUB) - (C – A) = (AU B) - (CN A°) by = (AUB)n (CN A^)° by = (AU B) N (C° U(A°)*) by = (AU B)n (CUA)

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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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

For all sets A, B, C.Then: (AU B)- (C - A) = AU(B – C).
The following algebraic proof is almost finished. You must provide a reason for every step that exactly justifies what was done in the step.
(Fill the number into the box)
As a reminder the 12 rules are:
1. Commutative Law
2. Associative Law
3. Distributive Law
4. Identity Law
5. Complement Law
6. Double Complement Law
7. Idempotent Law
8. Universal Bound Law
9. De Morgan's Law
10. Absorption Law
11. Complements of U and Empty Set
12. Set Difference Law
Proof: Let A, B,C be any sets. Then:
by
LHS = (AU B) - (C – A) = (AUB) - (Cn A°)
by
= (AUB)n (Cn A°)°
%3D
by
= (AU B)n(Ce U (A°))
by
= (AUB)n (C U A)

Is the following proposition true or false?
For all sets A and B :
A x (B – A) = A x B.
(Select all the choices that apply)
No, and I can disprove it by finding a counterexample.
O Yes, and I can prove it using the element method.
O Yes, and I can prove it using the algebraic method.
| cannot tell with the given information.

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