HWSet-Chapter5

HWSet-Chapter5 - Math 326 Fall 2010 Homework Set Chapter 5...

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Unformatted text preview: Math 326 Fall 2010 Homework Set Chapter 5 Solutions 1 5.1.7 Let A = { c,d,f,g } , B = { f,g } , and C = { d,g } . (a) Is B A ? Yes, because every element of B is in A . (b) Is C A ? Yes, because every element of C is in A . (c) Is C C ? Yes, because every element of C is in C . (d) is C a proper subset of C ? No, because there are no elements of C that are not in C . 5.1.8 (a) Is 3 { 1 , 2 , 3 } ? Yes (b) Is 1 { 1 } ? Yes (c) Is { 2 } { 1 , 2 } ? No (d) Is { 3 } { 1 , { 2 } , { 3 }} ? Yes (e) Is 1 { 1 } ? Yes (f) Is { 2 } { 1 , { 2 } , { 3 }} ? No, because 2 6 the set. (g) Is { 1 } { 1 , 2 } ? Yes (h) Is 1 {{ 1 } , 2 } ? No (i) Is { 1 } { 1 , { 2 }} ? Yes (j) Is { 1 } { 1 } ? Yes 5.1.11 Let A = { x R | - 3 x } , B = { x R | - 1 < x < 2 } , C = { x R | 6 < x 8 } . (a) A B = { x R | - 3 x < 2 } (b) A B = { x R | - 1 < x } (c) A C = { x R | x <- 3 x > } (d) A C = { x R | - 3 x 6 < x 8 } (e) A C = (f) B C = { x R | x - 1 x 2 } (g) A C B C = { x R | x <- 3 x 2 } (h) A C B C = { x R | x - 1 x > } (i) ( A B ) C = { x R | x - 1 x > } (j) ( A B ) C = { x R | x <- 3 x 2 } 5.1.12 True or False (a) Z + Q True (b) R- Q False (c) Q Z False (d) Z- Z + = Z False (missing 0) (e) Z- Z + = True (f) Q R = Q True (g) Q Z = Q True (h) Z + R = Z + True (i) Z Q = Z False 2 5.1.29 Let A = { x,y,z,w } and B = { a,b } . (a) A B = { ( x,a ) , ( x,b ) , ( y,a ) , ( y,b ) , ( z,a ) , ( z,b ) , ( w,a ) , ( w,b ) } (b) A A = { ( x,x ) , ( x,y ) , ( x,z ) , ( x,w ), ( y,x ) , ( y,y ) , ( y,z ) , ( y,w ), ( z,x ) , ( z,y ) , ( z,z ) , ( z,w ), ( w,x ), ( w,y ), ( w,z ), ( w,w ) } (c) B A = { ( a,x ) , ( a,y ) , ( a,z ) , ( a,w ) , ( b,x ) , ( b,y ) , ( b,z ) ,...
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HWSet-Chapter5 - Math 326 Fall 2010 Homework Set Chapter 5...

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