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### Number and algebra

### Geometry and measure

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### Working mathematically

### For younger learners

### Advanced mathematics

# Groups Further

### Groups of Sets

### Poison, Antidote, Water

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Age 16 to 18

Challenge Level

The binary operation * for combining sets is defined as the union of two sets minus their intersection. Prove the set of all subsets of a set S together with the binary operation * forms a group.

Age 14 to 18

Challenge Level

Play the game of Poison, Antidote, Water to start to understand the mathematics of associativity and groups.