Answer to Question #129223 in Discrete Mathematics for Amir

Question

a) 04 points Draw Venn diagram to describe sets A, B, and C that satisfy the given conditions. AC B, CC B, AnC +0. (b) 03 points For each integer m, let Tm = {m2, m*}. How many elements are in each of T-3, T-1, To, T1? Give justification. (c) 03 points Let A = {-2,0, 2}, B = {4,6, 8} and define a relation T from A to B as follows: For all (r, y) E A x B, (r, y) € T means that is an integer. Write T as a set of ordered pairs and find the %3! %3D %3D domain and co-domain of T

Answer 1

a)

b) Tm = {m2, m*}.

T(-3) consist of 2 elements - {9,-3}

T(-1) consist of 2 elements - {1,-1}

T(0) consist of {0,0}

T(1) consist of {1,1}

c)V={(x,y)$\in$ G×H$\mid$ (x-y)/4 is integer }

V contains all ordered pairs (x,y)$\in$ (G,H) for which (x-y)/4 is an integer and thus if the difference of x and y is divisibe by 4.

When x=-2$\in$ G, then x-y is ony divisible by 4 for y=6 $\in$ H.

(-2,6)$\in$ V

When x=0$\in$ G, then x-y is only divisible by 4 for y=4$\in$ H and y=8$\in$ H

(0,4)$\in$ T

(0,8)$\in$ T

When x=2$\in$ G, then x-y is only divisible by 4 for y=6$\in$ H

(2,6)$\in$ T

V then contains all previously mentioned ordered pairs

V={(-2,6),(0,4),(0,8),(2,6)}

The domain of V contains all values x for which (x,y)$\in$ V. By previous part we then note that x can take on the values -2,0,2.

Domain={-2,0,2}

The codomain of V contains all values y for which (x,y)$\in$ V. We then note that y can take on the values 4,6,8.

Codomain={4,6,8}