&o Theorem 3. 1: Let f be a(everywhere) function from a to b and a and a be subsets of a. then %(1)IfAcA2, then f(ADcf(a2) (2)f(A1∩A2)∈f(A1)nf(A2) (3)f(A1UA2)=f(A1)∪f(A2) (4)f(A1)-f(A2)∈f(A1-A2) o Proof: 3)(a)f(AlUf(ACfA, UA2) 令(b)fA1UA2)∈fA1Uf(42)❖Theorem 3.1: Let f be a (everywhere) function from A to B, and A1 and A2 be subsets of A. Then ❖(1)If A1A2 , then f(A1 ) f(A2 ) ❖(2) f(A1∩A2 ) f(A1 )∩f(A2 ) ❖(3) f(A1∪A2 )= f(A1 )∪f(A2 ) ❖(4) f(A1 )- f(A2 ) f(A1 -A2 ) ❖ Proof: (3)(a) f(A1 )∪f (A2 ) f(A1∪A2 ) ❖ (b) f(A1∪A2 ) f(A1 )∪f (A2 )