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8 problems: (1) 'Is (ℤ, subtraction) a group? Which axiom fails?' (Not associative: (a-b)-c ≠ a-(b-c)). (2) 'Is ({1,-1,i,-i}, ×) a group?' (Yes! Verify all 4 axioms). (3) 'Find all elements and their orders in ℤ₆ = {0,1,2,3,4,5} under addition mod 6.' (4) 'Complete the Cayley table for ℤ₄.' (5) 'Wha

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