Further Mathematics 7367: Binary Operations Topical Past Paper Questions

(a) By considering associativity, show that the set of integers does not form a group under the binary operation of subtraction. Fully justify your answer. [2 marks] (b) The group G is formed by the set {1, 7, 8, 11, 12, 18} under the operation of multiplication modulo 19 (b)(i)…

The group $ (C, +4) $ contains the elements 0, 1, 2 and 3 (a) (i) Show that C is a cyclic group. [2 marks] (a) (ii) State the group of symmetries of a regular polygon that is isomorphic to C [1 mark] (b) The group $(V, \otimes)$ contains the elements (1, 1), (1, -1), (-1, 1) and…

The binary operation $ \oplus $ acts on the positive integers x and y such that $$ x\oplus y=x+y+8\pmod{k^{2}-16k+74} $$ where k is a positive integer. Show that $\oplus$ is commutative. [1 mark] (a) (ii) Determine whether or not Ⓤ is associative. Fully justify your answer. [2 ma…