令A(yù)={1,2,3,4 },下列關(guān)系是否是自反的、反自反的、對稱的、反對稱的、傳遞的? (1)R={(1,1),(1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4)} (2)Φ (3)R={(1,2),(1,3),(3,1),(1,1),(3,3),(3,2),(1,4),(4,2),(3,4)}
(1)自反、對稱、傳遞 (2)反自反、對稱、不對稱、反對稱、傳遞 (3)傳遞
令A(yù),B,C是實(shí)數(shù)集合,f:A→B和g:A→B定義為,f (a)=a+1,g(b)=b2+2給出: (1)(f ◦g)(2) (2)(g ◦f)(2) (3)(f ◦g)(x) (4)(g ◦f)(x) (5)(f ◦f)(x) (6)(g ◦g)(x)
對于以下給定的結(jié)構(gòu),如果存在,求出其幺元。 (1)結(jié)構(gòu)< 實(shí)數(shù)集合,+,* >; (2)結(jié)構(gòu)< 集合的集合,∪,∩,->