Question: 7. Let A be a nonempty set. Let S and T be relations on A. Show that if S is transitive and T is transitive,

7. Let A be a nonempty set. Let S and T be relations on A. Show that if S is transitive and T is transitive, then S T is transitive 8. Let S={(x,y)ZZ|2x+3y=5z,some zZ} and K = {(x,y) Z Z|2x + y = 3k some k Z} Accept that both are equivalence relations on Z. Is S K an equivalence relation on Z? 9. Let S = {(x,y) IN IN|2x+3y = 30, some z IN}. Find the elements of SS 10. Let A = {1,2,3,4,5,6,7,8,9,10}. Let T = {(a,b) AA|5a+3b = 8c some c Z} Accept that this is an equivalence relation on A. Determine all the elements in the class of 1. Show how you obtain them. Determine all the elements in the class of 5 (Justify that there are no others apart from those found)

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