6. Let A, B, and D be arbitrary stes. Write each of the following sets in...

  

Transcribed Image Text:

6. Let A, B, and D be arbitrary stes. Write each of the following sets in terms of A, B, and D and the operations U, and complement. (a) E= {x: x E D (r E AVIE B)} (b) F = {r: (x E AAr E D) = e B} 7. Prove : An (AU B) = A. 8. Prove : ACB AUB= B. 9. Prove that AU(B- A) = AUB. (a) With the pick-a-point method. (b) With an algebraic proof (distributive law). 10. Prove that the following statements are logically equivalent. (a) ACB (b) A°UB =U (c) AN B = =D0. 11. Let A = {An : n= 1,2, 3...}, where A, =-1,1 %3D (a) Find A and prove your conjecture. (b) Find UA and prove your conjecture. 6. Let A, B, and D be arbitrary stes. Write each of the following sets in terms of A, B, and D and the operations U, and complement. (a) E= {x: x E D (r E AVIE B)} (b) F = {r: (x E AAr E D) = e B} 7. Prove : An (AU B) = A. 8. Prove : ACB AUB= B. 9. Prove that AU(B- A) = AUB. (a) With the pick-a-point method. (b) With an algebraic proof (distributive law). 10. Prove that the following statements are logically equivalent. (a) ACB (b) A°UB =U (c) AN B = =D0. 11. Let A = {An : n= 1,2, 3...}, where A, =-1,1 %3D (a) Find A and prove your conjecture. (b) Find UA and prove your conjecture.