Neco 2020 Further Mathematics Question 1

Practice essay / theory question 1 from the 2020 Neco Further Mathematics examination. This question covers Sets, Functions, Binary Operations .

Neco 2020 Further Mathematics Essay / Theory

Topics: Sets Functions Binary Operations

Question 1 NECO • 2020 • FURTHER_MATHEMATICS • essay

Consider the universal set \(U = \{1,2,3,4,5,6,7,8,9,10\}\). Let \(A = \{x \in U \mid x \text{ is a multiple of 2}\}\) and \(B = \{x \in U \mid x > 4\}\). Define a binary operation \(\) on the set \(S = \{1,2,3,4,5\}\) by \(a b = (a + b) \bmod 5\), where the result \(0\) is identified with \(5\).

( a )

List the elements of sets \(A\) and \(B\). Then find \(A \cap B\) and \(A \cup B\).

( b )

Find the cardinality of the complement of \(A \cup B\) in \(U\).

( c )

Construct the operation table for \(*\) on \(S\).

( d )

State whether \(*\) is associative on \(S\). Justify your answer with a brief verification using any three elements of \(S\).

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This is Neco 2020 Further Mathematics Question 1. It is one of the essay questions from the 2020 Neco Further Mathematics examination.

The question covers Sets, Functions, Binary Operations .

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