I'm an engineer, not a mathematician... the professor has assigned several proof questions, and I'm having difficulty answering them... (This may need to be moved to homework help, but the topic is unusual, so I thought I'd get better response here) Terminology: v is a join operation, ^ is a meet operation D is a bracket operation Example: Show that when: [tex] A = a_1 \vee a_2, B = b_1 \vee b_2, \ and\ n = 2 [/tex] then [tex] A \wedge B = -D[a_2 , b_1 , b_2] a_1 + D[a_1 , b_1 , b_2] a_2 [/tex] [tex]= D[a_1 , a_2 , b_2] b_1 - D[a_1 , a_2 , b_1] b_2 [/tex] If the meet is zero, then assuming that the sets [itex] (a_1, a_2) [/itex] and [itex] (b_1, b_2) [/itex] are both independent, the four brackets must be zero. Show that, in this case, the two subspaces [itex] A_s[/itex] and [itex] B_s [/itex] are the same. Now, proving the first part is fairly simple: just run though the definition of the meet. I'm having difficulty with the second part. I thought that the definition of the meet is the intersection of the two subspaces. If the subspaces are the equal, then wouldn't the meet be either As or Bs?