equivalence relations -- proof writing examples 17

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[DisneyPlayhousetv]

For question 2 you keep saying equivalence classes. Are these not equivalence relations?

[r.maelstrom]

For the x = y mod 5:
5|2x+3y, so 2x+3y=0 mod 5. That is 2x = -3y mod 5. But -3=2 mod 5, so we have 2x = 2y mod 5 and 2·3x = 2·3y mod 5, which is x = y mod 5, for 3 is mult inverse of 2 in the 5Z group.