1. On a sheet of paper, solve the following Problem involving sets. Please show all of your work, including any computations that you may have done by calculator or in your head.

Tyrell owns a start-up company that is not yet turning a profit. As such, he is spending some of his savings every month to keep the business going.

Tyrell’s personal budget consists primarily of three overlapping monthly budget categories: work-related expenses, home-related expenses, and items charged to his credit card.

Given the following information from last April, find how much he spent that is not in any of the three categories (for example on a gift for Tyrell’s special someone that was purchased with cash).

Tyrell spent:

  • $2265 total
  • $768 on all work-related expenses
  • $1223 on all home-related expenses
  • $519 on all expenses charged to his credit card
  • $253 on expenses that are both work and home-related
  • $288 on work-related expenses charged to his credit card
  • $129 on home-related expenses that are charged to his credit card
  • $73 on expenses that are work-related, home-related, and charged to his credit card
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