推 fj90406:謝謝大大解惑^^ 04/01 08:25
※ 引述《sodas2002 (sodas)》之銘言：
: ※ 引述《fj90406 (阿亮)》之銘言：
: : Let A = Z+ * Z+ a relation R on A as follows:
: : (x,y)R(u,v) if and only if x*v=y*u.
: : (1) Prove that R is an equivalent relation.
: For All x,y ∈Z+, x*y=y*x
: --> (x,y)R(x,y) --> Reflexive
: For All x,y,z,w ∈Z+, if x*w=y*z, then z*y=w*x
: --> ∀(x,y)R(z,w) ∃(z,w)R(x,y) --> Symmetric
: For All x,y,z,w,a,b∈Z+, if ∃(x,y)R(z,w)^(z,w)R(a,b)
: --> x*w=y*z ^ z*b=w*a
: ,,,,, No Transitive
: So, this is not an equivalent relation.
: : (2) Computer the equivalence class of (5,4)
: Not exists.
設(x,y)為(5,4)之等價類元素
=> 4x = 5y
=> x = 5k
y = 4k , k屬於N
Ans: [(5,4)] = {(5k,4k)|k屬於N}
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