Answer to Question #171723 in Discrete Mathematics 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

A=$\{\pi,e,0\}, B=\{0,1\}$

2.

$a) A\times B=\{(\pi,0),(\pi,1),(e,0),(e,1),(0,0),(0,1)\}$

b) B$\times A=\{(0,\pi),(0,e),(0,0),(1,\pi),(1,e),(1,0)\}$

c)$A\times A=\{(\pi,\pi),(\pi,e),(\pi,0),(e,e),(e,0),(0,0)\}$

$d) B\times B=\{(0,0),(0,1),(1,0),(1,1)\}$

e)$\phi\times B=\phi$

f)$(A\times B)\times B=\{(\pi,0,0),(\pi,0,1),(\pi,1,0),(\pi,1,1),(e,0,0),(e,0,1),(e,1,0),(e,1,1),(0,0,0),(0,0,1)\}$

g)$A\times (B\times B)=(A\times B)\times B$

h)$A\times B\times B= (A\times B) \times B=A\times (B\times B)$

4.

{nϵZ:2<n<5}x{nϵZ:│n│=5}=$\{(3,5),(3,-5),(4,5),(4,-5)\}$