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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)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.3: Introduction To Geometric Proof
Problem 23E: In Exercises 23 to 24, fill in the missing reasons for the algebraic proof. Given: 3(x5)=21 Prove:...
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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)
Transcribed Image Text: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.
Transcribed Image Text: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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