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(BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are sets, then A- 13. If A,B and C are sets, then A-(BUC)=(A-B) n(A-C). 14. If A,B and C are sets, then (AUB)-C=(A-C)u(B-C). 15. If A, B and C are sets, then (AnB)-C=(A-C)n(B-C). 16. If A, B and C are sets, then A x (BUC) = (A x B)U(A x C). 17. If A,B and C are sets, then Ax (BOC) = (A x B) n(Ax C). 18. If A, B and C are sets, then Ax (B-C) = (A x B)-(A x C). 19. Prove that {9":ne Z} = {3":ne Z}, but {9" : ne Z} # {3":n€Z} 20. Prove that {9":ne Q} = {3":ne Q}.

(BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are sets, then A- 13. If A,B and C are sets, then A-(BUC)=(A-B) n(A-C). 14. If A,B and C are sets, then (AUB)-C=(A-C)u(B-C). 15. If A, B and C are sets, then (AnB)-C=(A-C)n(B-C). 16. If A, B and C are sets, then A x (BUC) = (A x B)U(A x C). 17. If A,B and C are sets, then Ax (BOC) = (A x B) n(Ax C). 18. If A, B and C are sets, then Ax (B-C) = (A x B)-(A x C). 19. Prove that {9":ne Z} = {3":ne Z}, but {9" : ne Z} # {3":n€Z} 20. Prove that {9":ne Q} = {3":ne Q}.

Advanced Engineering Mathematics
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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Prove the following

 


answer #12 only

11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A,B and C are sets, then A- (BOC)=(A-B)u(A-C). 13. If A,B and C are sets, then A-(BUC)=(A-B) n(A-C). 14. If A,B and C are sets, then (AUB)-C=(A-C)u(B-C). 15. If A,B and C are sets, then (AnB)-C=(A-C)n(B-C). 16. If A, B and C are sets, then Ax (BUC) = (A x B)U(AXC). 17. If A,B and C are sets, then Ax (BOC) = (A x B) n(Ax C). 18. If A, B and C are sets, then Ax (B-C) = (A x B)-(A x C). 19. Prove that {9":ne Z} = {3":ne Z}, but {9" : ne Z} # {3":n€Z} 20. Prove that {9":ne Q} = {3":ne Q}.
Transcribed Image Text:11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A,B and C are sets, then A- (BOC)=(A-B)u(A-C). 13. If A,B and C are sets, then A-(BUC)=(A-B) n(A-C). 14. If A,B and C are sets, then (AUB)-C=(A-C)u(B-C). 15. If A,B and C are sets, then (AnB)-C=(A-C)n(B-C). 16. If A, B and C are sets, then Ax (BUC) = (A x B)U(AXC). 17. If A,B and C are sets, then Ax (BOC) = (A x B) n(Ax C). 18. If A, B and C are sets, then Ax (B-C) = (A x B)-(A x C). 19. Prove that {9":ne Z} = {3":ne Z}, but {9" : ne Z} # {3":n€Z} 20. Prove that {9":ne Q} = {3":ne Q}.
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