大师作文网Show that the relation R consisting of all pairs(x,y) such t
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Show that the relation R consisting of all pairs(x,y) such that x and y are bit strings of length three or more that agree in their first three bits is an equivalence relation on the set of all bit strings of length three of more.
译文
证明由所有序偶(x,y)组成的关系R是全部长度等于3和大于3的字节串构成集合上的等价关系,其中x和y是长度等于3和大于3的字节串且它们前3个字节相同.
证明 显然关系具有自反性,对任意字节串x,它与它自身前3个字节相同.故R是自反的;如果x和y有关系R,则x和y的前3个字节相同,也即y和x的前3个字节相同,故R是对称的;如果x和y有关系R,y和z有关系R,则x和y的前3个字节相同,y和z的前3个字节相同,于是x和z的前3个字节也相同,故R是传递的,由A是自反的,对称的和传递的,则A是等价关系.
证明由所有序偶(x,y)组成的关系R是全部长度等于3和大于3的字节串构成集合上的等价关系,其中x和y是长度等于3和大于3的字节串且它们前3个字节相同.
证明 显然关系具有自反性,对任意字节串x,它与它自身前3个字节相同.故R是自反的;如果x和y有关系R,则x和y的前3个字节相同,也即y和x的前3个字节相同,故R是对称的;如果x和y有关系R,y和z有关系R,则x和y的前3个字节相同,y和z的前3个字节相同,于是x和z的前3个字节也相同,故R是传递的,由A是自反的,对称的和传递的,则A是等价关系.
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