学帮网设集合A={x│(x-3)(x-a)=0,a∈R},B={x│(x-4)(x-1)=0},求A∪B,A∩B,最好有过程,
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设集合A={x│(x-3)(x-a)=0,a∈R},B={x│(x-4)(x-1)=0},求A∪B,A∩B,最好有过程,
A ={x│(x-3)(x-a)=0,a∈R}
={3,a}
B ={x│(x-4)(x-1)=0}
= {1,4}
A∪B = {3,a}∪{1,4}
= {1,3,4,a,a∈R }
= R (∵ a is any real number )
A∩B = {3,a}∩{1,4}
= {1,4}