Answer to Question #171729 in Algebra for Mary-Ann Asuncion

Question

1.      Suppose A={4,3,6,7,1,9}, B={5,6,8,4} and C={5,8,4}. Find:

(a)   A ∪ B

(e) B-A

(h) B ∪ C

3. Suppose A={0,1} and B={1,2}. Find:

(a) (AxB) ∩(BxB)

(d) (A∩B)xA

(i) ℙ(AxB)

6. Sketch the sets X=[-1,3]x[0,2] and Y=[0,3]x[1,4] on the plane R². On separate drawings, shade in the sets X∪Y, X∩Y, X-Y and Y-X.

10. Do you think the statement (R-Z)xN=(RxN)-(Z-N) is true, or false? Justify.

Answer 1

1. Suppose $A={4,3,6,7,1,9},$ $B={5,6,8,4}$ and $C={5,8,4}.$ Find:

(a)  $A ∪ B = {1,3,4,5,6,7,8,9}$

(e) $B-A = {5,8}$

(h) $B ∪ C = {5,6,8,4}$

3. Suppose $A={0,1}$ and $B={1,2}$ . Find:

(a) $(AxB) ∩(BxB) = {(1,1),(1,2)}$

(d) $(A∩B)xA = {(1,0),(1,1)}$

(i) $ℙ(AxB) = \empty ,{(0,1)},{(0,2)},{(1,1)},{(1,2)},{(0,1),(0,2)},{(0,1),(1,1)},{(0,1),(1,2)},{(0,2),(1,1)},$

${(0,2),(1,2)},{(1,1),(1,2)},{(0,2),(1,1),(1,2)},{(0,1),(1,1),(1,2)},{(0,1),(0,2),(1,2)},$

${(0,1),(0,2),(1,1)}, {(0,1),(0,2),(1,1),(1,2)}$

6.

10.No because $(R-Z)xN = (RxN) - (ZxN)$

which means that $(RxN) - (ZxN)$ is not equal to $(RxN)-(Z-N)$