5.18 SHOW that AUB = (A |B)UB 5.17 If AUB =U. Show that %3D

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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سية العراق
فرحان المياحی- قسم
كلية العلوم / جامعة القادسية
Foundations of Mathematics I
محاضرة )5(
(1)
دراسات أولية مستوى أول
نظرية :3 مناقشة :1 عدد وحدات :3
5.16 show that AUB = (A |B)UB
5.17 If AUB =U. Show that A CB
5.18 show that (4B)U(ANBY = A
5.19 If A CB. Show that A U(B |A) = A
5.20 If A AC = BAC. Show that A = B.
5.21Find the value of x,y if V -2,2x +1) = (x -1,y+2)
5.20 Let A = {1,2,3}, B = (3,4,5), C = {1,3,5,8}. Find
AxA, Ax(B UC), (AxB)U(A xC), AxB xC, A
(4 x B)(A xC), Ax(BC), (AUB)x(BUC), (Ax
5.21 Let A,B,C be sets such that A = BOC. Prove or diprove
1. AxA (B x B)C xC)
- 2. AxA = (B xC)n(C xB)
5.22 Let A,B,C be sets. Show that
-1. (A xA)(B xC) = (AB)x(A nC)
2. (A x B)|(C xC)= ((A |C)xB)U(A x(B |C))
- 3. (A x4)|(B xC) = ((A | B ) × A)U(A ×(A |C).
5.23 Let A,B.C,D be sets. Show that
1. (A x B)n(C xD)= (A xD)n(C x B)
- 2. (A xB)n(C ×D)= (AnC)x(BOD)
A CCD AxC c
A xC = B × D
xD
-3. ACB
-4. A = B ^C = D >
-5.24 Show that if A xB = A xC and A #0, then B C
5.25 Show that if A xA = B xB, then A = B
5.26 Let A, B.C be three sets such that ACB. Show that A
-5.27 Given an example of three sets 4,B.C such that AU(B
د
62
Transcribed Image Text:سية العراق فرحان المياحی- قسم كلية العلوم / جامعة القادسية Foundations of Mathematics I محاضرة )5( (1) دراسات أولية مستوى أول نظرية :3 مناقشة :1 عدد وحدات :3 5.16 show that AUB = (A |B)UB 5.17 If AUB =U. Show that A CB 5.18 show that (4B)U(ANBY = A 5.19 If A CB. Show that A U(B |A) = A 5.20 If A AC = BAC. Show that A = B. 5.21Find the value of x,y if V -2,2x +1) = (x -1,y+2) 5.20 Let A = {1,2,3}, B = (3,4,5), C = {1,3,5,8}. Find AxA, Ax(B UC), (AxB)U(A xC), AxB xC, A (4 x B)(A xC), Ax(BC), (AUB)x(BUC), (Ax 5.21 Let A,B,C be sets such that A = BOC. Prove or diprove 1. AxA (B x B)C xC) - 2. AxA = (B xC)n(C xB) 5.22 Let A,B,C be sets. Show that -1. (A xA)(B xC) = (AB)x(A nC) 2. (A x B)|(C xC)= ((A |C)xB)U(A x(B |C)) - 3. (A x4)|(B xC) = ((A | B ) × A)U(A ×(A |C). 5.23 Let A,B.C,D be sets. Show that 1. (A x B)n(C xD)= (A xD)n(C x B) - 2. (A xB)n(C ×D)= (AnC)x(BOD) A CCD AxC c A xC = B × D xD -3. ACB -4. A = B ^C = D > -5.24 Show that if A xB = A xC and A #0, then B C 5.25 Show that if A xA = B xB, then A = B 5.26 Let A, B.C be three sets such that ACB. Show that A -5.27 Given an example of three sets 4,B.C such that AU(B د 62
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