OCR
Further Additional Pure AS
2017
December
— Question 4
Exam Board
OCR
Module
Further Additional Pure AS (Further Additional Pure AS)
Year
2017
Session
December
Topic
Groups
4
The binary operation is defined on \(\mathbb { Z }\) by \(a\) b \(b = a + b - a b\) for all \(a , b \in \mathbb { Z }\). Prove that is associative on \(\mathbb { Z }\).
The operation ∘ is defined on the set \(A = \{ 0,2,3,4,5,6 \}\) by \(a \circ b = a + b - a b ( \bmod 7 )\) for all \(a , b \in A\).
Complete the Cayley table for \(\left( A , { } ^ { \circ } \right)\) given in the Printed Answer Booklet.
Prove that \(( A , \circ )\) is a group. You may assume that the operation is associative.