Problem #2370

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$A$, $B$, and $C$ are sets such that $A \cup C = \{1,2,3,4,5,6\}$, $B \cup C = \{1,2,3,4\}$, $A \cap C = \emptyset$, $A \cap B = \{3\}$, and $B \cap C = \{1,2\}$. Find the product of the elements in $B$.

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Instructions for entering answers:

  • Reduce fractions to lowest terms and enter in the form 7/9.
  • Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
  • Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
  • Exponents should be entered in the form 10^10.
  • If the problem is multiple choice, enter the appropriate (capital) letter.
  • Enter points with parentheses, like so: (4,5)
  • Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).

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