21.-40. Imagine two coins on a table, at positions A and B. In this game there are eight possible moves: M1: Flip over the coin at A. M2: Flip over the coin at B. M3: Flip over both coins. M4: Switch the coins. M5: Flip coin at A; then switch. M6: Flip coin at B, then switch. M7: Flip both coins; then switch. E Do not change anything. We may consider an operation on the set I, M1, ..., M7), which consists of performing any two moves in succession. For example, if we switch coins, then flip over the coin at A, this is the same as first flipping over the coin at B then switching: M4* M1 = M2 M4 = M6 a. If G= {I, M1, ..., M7) and is the operation we have just described, write the table of (G, *). I M1 M2 M3 M4 M5 M6 M7 I M1 M2 M6 M3 M4 M6 M5 M6 M7

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