Neco 2017 Further Mathematics Question 1

Practice essay / theory question 1 from the 2017 Neco Further Mathematics examination. This question covers Sets, Functions, Binary Operations .

Neco 2017 Further Mathematics Essay / Theory

Topics: Sets Functions Binary Operations

Question 1 NECO • 2017 • FURTHER_MATHEMATICS • essay

Let \(A=\{1,2,3,4,5\}\). A binary operation \(\) is defined on \(A\) by \[a b = (a + 2b) \bmod 5,\] where the result of the modulo operation is taken to be an element of \(A\) (the value \(0\) is replaced by \(5\)).

( a )

Show that the operation \(*\) is closed on \(A\).

( b )

Determine whether an identity element \(e\) exists for \(*\) on \(A\). If it exists, find its value.

( c )

Find the inverse of the element \(3\) under \(*\) (if it exists).

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This is Neco 2017 Further Mathematics Question 1. It is one of the essay questions from the 2017 Neco Further Mathematics examination.

The question covers Sets, Functions, Binary Operations .

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