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Consider the given universal set T and its subjects C, D and E
T = {0, 2, 4, 6, 8, 10, 12}
C = {4, 8,}
D = {10, 2, 0}
E = {0}
Find out
ii) D ∩ E
iii) C ∩ D ∩ E
a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain t
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Let D(subscript12) = ({x,y : x^2 = e ; y^6 = e ; xy =(y^-1) x}) a) Which of the following subsets are subgroups of D(subscript12) ? Justify your answer. i) {x,y,xy,y^2,y^3,e}
Find the solution to the following system of equations using substitution:
Solution i) D ∩ E = {10, 2, 0} ∩ {0} = {0} ii) C ∩ D ∩ E = {4, 8} ∩ {10, 2, 0} ∩ {0} = { } = Ø
Solution
i) D ∩ E = {10, 2, 0} ∩ {0} = {0}
ii) C ∩ D ∩ E = {4, 8} ∩ {10, 2, 0} ∩ {0} = { } = Ø
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