In this final section we look at a method of classifying the elements of a set by sorting them into subsets. We shall require that the set is sorted into disjoint subsets â€“ so each element of the set belongs to exactly one subset. Such a classification is known as a partition of a set. In order to achieve a partition, we need to have a method which enables us to decide whether or not one element belongs to the same subset as another. We look first at the general idea of a r
Author(s): The Open University

Try some yourself

## Question 1

Draw a line of symmetry on each of the shapes below.

2.7 Rotational symmetry

There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.

Look at the trim on the left. It does not have line symmetry but
Author(s): The Open University

A quadrilateral is a shape with four straight sides.
Author(s): The Open University

1.4 Parallel lines

Two straight lines that do not intersect, no matter how far they are extended, are said to be parallel. Arrows are used to indicate parallel lines.

Author(s): The Open University

1.3.3 Drawing a pie chart

You can use the fact that the sum of angles at a point is 360Â° to draw a pie chart.

## Example 4

Over a five-year period a mathematics tutor found that 16 of her students gained distinctions, 32 gained pass grades and 12 failed to complete the course. Draw a pie chart to re
Author(s): The Open University

4.4 ‘Show that ’ questions

In this type of question you are given the answer! All the marks are allocated for correct reasoning and justification.

## Example 15

Suppose you now decide to place your new bath (length 1.7 m, height 0.8 m) against this wall as shown in the diagram below.

Author(s): The Open University

Keep on learning

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## Study another free course

There are more thanÂ 800 coursesÂ on OpenLearnÂ for you to
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Learning outcomes

After studying this course, you should be able to:

• relate the temperature of a solid to the mean kinetic energy of its atoms

• use models for thermally induced effects that involve linear, exponential and step changes

• use exponentials, logarithms and graphical methods to interpret data from a thermally activated process in terms of Arrhenius's law

• identify the changes of phase taking place in a variety of critical phenomena

• Author(s): The Open University

2.3 Inverse proportion

In Section 2.2 you saw that direct proportion described relationships between two quantities, where as one increased, so did the other. Sometimes as one quantity increases the other decreases instead of increasing. This is called indirect proportion. Team tasks are often an example of this. The ti
Author(s): The Open University

Surface water
Water is arguably the most important physical resource as it is the one that is essential to human survival. Understanding the global water cycle and how we use water is essential to planning a sustainable source of water for the future. In the UK there are areas where water supplies are limited, as shown by recent droughts. Globally, there are many areas that do not have enough water to support the current population adequately. Decisions will have to be made on the best way to use water in a w
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Logframe planning
As a way of thinking about projects, Logical Framework Analysis helps to focus on some key questions during the project design process. This free course, Logframe planning, improves your understanding of and practice with the structure of the logframe matrix using an animated overview with voice-over commentary followed by interactive questions relating to using the matrix. Author(s): Creator not set

iSpot: Sharing nature
This free course, iSpot: Sharing nature, provides a valuable resource for anyone with an interest in nature. It will give you the opportunity to learn more about wildlife, and to share your interest with a wider community. First published on Wed, 21 Jun 2017 as Author(s): Creator not set

Introduction

This unit explores different understandings of nature and environment and the significance these may have for developing responsibility. The problems of connecting human and non-human nature are presented here as being a challenge peculiar to the concerns of environmental responsibility. They provide the impetus for exploring the idea of â€˜conversationâ€™ as a metaphor for what matters in environmental responsibility. Using a reading by Stephen Talbott as a foundation, the conversation me
Author(s): The Open University

Water for life
Atoms, elements and molecules are the building blocks of everything that makes up our world, including ourselves. In this free course, Water for life, you will learn the basic chemistry of how these components work together, starting with a chemical compound we are all very familiar with water. First published on Wed, 17 Jan 2018 as Author(s): Creator not set

Financial methods in environmental decisions
This free course, Financial methods in environmental decisions, begins by introducing some of the tools that can be used to assess the benefits of investment decisions, including ways of assessing the â€˜external costsâ€™ â€“ the wider costs and benefits to society as a whole â€“ of environmental decisions. First published on Thu, 29 Nov 2018 as Author(s): Creator not set

The science of nuclear energy
This free course, The science of nuclear energy, will delve into the science behind nuclear power and explain what happens inside a nuclear reactor and what it means for an element to be radioactive. It will explore some of the risks of producing nuclear power and examine the arguments for and against including it in future energy planning as well as looking at other potential future solutions. Author(s): Creator not set

Eutrophication
Managing eutrophication is a key element in maintaining the earths biodiversity. Eutrophication is a process mostly associated with human activity whereby ecosystems accumulate minerals. This free course, Eutrophication, explains how this process occurs, what its effects on different types of habitat are, and how it might be managed. First published on Mo
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2.1 Dealing with change in what matters: ethics, policy and action

Much of what has been covered so far in this unit deals with the individual human capacity to frame nature as a means for enabling environmental responsibility. But what are the implications of this for actually doing something about policy design and action to improve matters? Framing the natural world is an inevitable human endeavour that we all carry out, whether consciously or subconsciously, as part of our interaction with human and non-human nature. For example, each of the tools listed
Author(s): The Open University

1.4.2 Engaging with multiple perspectives

A systems approach begins when first you see the world through the eyes of another.

(Churchman, 1968, p. 231)

The Ulrich reading is an extract from an article written in honour of another systems philosopher, C. West Churchman. Also drawing on Churchman's influence, Jake Chapman sums up two qualities of systems thinking in terms of â€˜gaining a bigger picture (going up a level of abstraction) a
Author(s): The Open University