Assignment #2 Due June 2 1998

Section 1.4 – 2,8,18

Section 1.5 – 4,8

  1. Let f(x) be a strictly increasing function. Show that f(x) is one-to-one.
  2. Let A,B,C be sets over the same domain. Prove that
  3. (A B) C = A (B C) if and only if C A.

  4. In chess, the king can move one position in any direction. Assuming that the king is moved only in a forward manner (one position up, to the right, or diagonally northeast), along how many different paths can a king be moved from the lower left corner position to the upper right corner position on the standard 8X8 chessboard?