You might guess, by analogy with the formula for the number of elementsin the union of
Chapter 2, Problem 17(choose chapter or problem)
You might guess, by analogy with the formula for the number of elementsin the union of three subsets of a finite set, that if U1; U2; U3 aresubspaces of a finite-dimensional vector space, thendim.U1 C U2 C U3/D dim U1 C dim U2 C dim U3 dim.U1 \ U2/ dim.U1 \ U3/ dim.U2 \ U3/C dim.U1 \ U2 \ U3/:Prove this or give a counterexample.
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