Question #129223
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
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Expert's answer
2020-08-16T20:56:50-0400

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}


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