Answer to Question #171725 in Algebra for Mary-Ann Asuncion

Question

A.     Write out the indicated sets by listing their elements between braces.

2. Suppose A={π,e,0} and B={0,1}

(a)   AxB

(b)  BxA

(c)   AxA

(d)  BxB

(e)  ØxB

(f)    (AxB)xB

(g)   Ax(BxB)

(h)  AxBxB

4. {nϵZ:2<n<5}x{nϵZ:│n│=5}

B. Sketch these Cartesian products on the x-y plane R².

10. {-1,0,1}x{1,2,3}

12. [-1,1]x[1,2]

14. [1,2]x{1,1.5,2}

16. [0,1]x{1}

Answer 1

Solution.

A.

2. $A=\{π,e,0\},B=\{0,1\}.$

(a) $A×B=\{(π,0),(π,1),(e,0),(e,1),\newline(0,0),(0,1)\}. \newline\text{(b)}$$B×A=\{(0,π),(0,e),(0,1),(1,π),\newline(1,e),(1,0)\}.$

(c)

$A×A=\{(π,π),(π,e),(π,0),(e,π),(e,e),(e,0),\newline(0,π),(0,e),(0,0)\}.$

(d)

$B×B=\{(0,0),(0,1),(1,0),(1,1)\}.$

(e)

$Ø×B=Ø.$

(f)

$(A×B)×B=\{(π,0,0),(π,0,1),(π,1,0),(π,1,1)\newline (e,0,0),(e,0,1),(e,1,0),(e,1,1) \newline (0,0,0),(0,0,1),(0,1,0),(0,1,1)\}.$

(g)

$A×(B×B)=\{(π,0,0),(π,0,1),(π,1,0),(π,1,1)\newline (e,0,0),(e,0,1),(e,1,0),(e,1,1) \newline (0,0,0),(0,0,1),(0,1,0),(0,1,1)\}.$

(h)

$A×B×B=\{(π,0,0),(π,0,1),(π,1,0),(π,1,1)\newline (e,0,0),(e,0,1),(e,1,0),(e,1,1) \newline (0,0,0),(0,0,1),(0,1,0),(0,1,1)\}.$

4.

$\{n\in Z|2<n<5\}×\{n\in Z| |n|=5\}=\{(3,-5),(3,-4),(3,-3),(3,-2)\newline (3,-1),(3,0),(3,1),(3,2),(3,3)\newline (3,4),(3,5),(4,-5),(4,-4),(4,-3) \newline (4,-2),(4,-1),(4,0),(4,1),\newline (4,2),(4,3),(4,4),(4,5)\}.$

B.

10.

12.

14.

16.