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ose 7. Suppose A, B and C are sets. If BC, then AXB≤AXC. 8. If A,B and C are sets, then AU(BnC)=(AUB) n(AUC). 9. If A,B and C are sets, then An (BUC)=(ANB)u(ANC). 10. If A and B are sets in a universal set U, then AnB=AUB.

ose 7. Suppose A, B and C are sets. If BC, then AXB≤AXC. 8. If A,B and C are sets, then AU(BnC)=(AUB) n(AUC). 9. If A,B and C are sets, then An (BUC)=(ANB)u(ANC). 10. If A and B are sets in a universal set U, then AnB=AUB.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.1: Ideals And Quotient Rings
Problem 20E: 20. If and are nonzero integers and is the least common multiple of and prove that.
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5. If p and q are positive integers, then {pn:neN} n {qn:n €N} #ø. 6. Suppose A,B and C are sets. Prove that if A≤B, then A-C<B-C. 7. Suppose A,B and C are sets. If B≤C, then A x B=AXC. 8. If A, B and C are sets, then Au(BnC)=(AUB)n(AUC). 9. If A, B and C are sets, then An (BUC)=(AnB)u(ANC). 10. If A and B are sets in a universal set U, then AnB=AUB. 11 AD 7-7
Transcribed Image Text:5. If p and q are positive integers, then {pn:neN} n {qn:n €N} #ø. 6. Suppose A,B and C are sets. Prove that if A≤B, then A-C<B-C. 7. Suppose A,B and C are sets. If B≤C, then A x B=AXC. 8. If A, B and C are sets, then Au(BnC)=(AUB)n(AUC). 9. If A, B and C are sets, then An (BUC)=(AnB)u(ANC). 10. If A and B are sets in a universal set U, then AnB=AUB. 11 AD 7-7
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