Abstract Algebra (AQA A-Level Further Maths): Quizzes

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Binary Operations
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What property must a function satisfy to be a binary operation on a set?

Closure

Is ab=aba \blacksquare b = \frac{a}{b} a binary operation on Z\mathbb{Z}?

No, 23\frac{2}{3} is not in Z\mathbb{Z}

What does it mean for a binary operation * to be commutative?

ab=baa * b = b * a for all aa and bb

Is the operation ab=aba \circledast b = a^b commutative on N\mathbb{N}?

No, 25522^5 \neq 5^2

What does it mean for operation * to be associative?

(ab)c=a(bc)(a * b) * c = a * (b * c) for all

What is the identity element for ab=a+ba * b = a + b on Q\mathbb{Q}?

00

For ab=a+ba * b = a + b on Q\mathbb{Q} with identity 00, which element is self-inverse?

00

In a Cayley table, how do you find bcb * c?

Row starting with bb, column headed by cc

How do you identify the identity element in a Cayley table?

Column identical to leftmost column

What does symmetry along the leading diagonal of a Cayley table indicate?

The operation is commutative

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