Learn about application Venn diagrams to array abstracts and recognise the agreement ‘universal set’, ‘member’ and ‘complement’.

This assignment includes:

Created in affiliation with GCSEPod

Venn diagrams are acclimated to array groups of data. They abide of 2 or added circles, generally overlapping, independent central a rectangle, like in the angel here.

Each amphitheater aural the diagram represents a set. The advice in a set could be fabricated up of a account of numbers, for example, or chase a assertive aphorism or accept a specific property.

A Venn diagram is acclimated to appearance the accord amid the altered items apparent in a cardinal of sets. These items are accepted as elements or associates of a set.

Example – Lemons and bananas

You could use a Venn diagram to appearance the differences and similarities amid lemons and bananas. You would accept a set assuming the elements of lemons, addition set assuming the elements of bananas, and the overlap assuming the set of aggregate elements.

Numbers can additionally be sorted into a Venn diagram. Where the numbers are placed on the diagram depends on the backdrop of the numbers. Anniversary cardinal apparent is an aspect or a affiliate of the set it belongs in.

A set of numbers can be authentic by a rule, or could artlessly be a account of numbers. Sometimes the alone affair that the numbers in a set accept in accepted is that they accord to a set with a accurate name.

When the set of numbers with a aggregate rule, or apparent as a list, that charge to be placed in a Venn diagram are accounting out, they are independent aural coiled brackets, like these: { … }.

Examples

Set E = {Odd numbers} – this set of numbers is authentic by a rule. In this case, all the numbers in ‘set E’ are odd.

Set F = {2, 4, 5, 9, 10} – this set of numbers does not chase a specific rule, and it does not amount why they are in the set.

Set G = {1,2,3…10} – this set is the integers, or accomplished numbers, from 1 up to, and including, 10.

Using ‘…’ is a beneath way of autograph the set, instead of accepting to address it out in full, ie ‘Set G = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}’.

Watch up to 1:33 in this abbreviate video from GCSEPod to apprentice added about allocation abstracts into a Venn diagram.

GCSEPod – Venn diagrams and allocation abstracts

The accepted set refers to all the ethics that charge to be advised in a accurate question. The accepted set is generally represented by the Greek letter epsilon, ε. All the associates of the accepted set charge be represented about central the rectangle in a Venn diagram.

The accompaniment of a set refers to all the elements which are not in a accurate set. It is represented as the name of the set, followed by a dash. For archetype A’ is the set of elements which are not in set A.

Example

Consider the accepted set ε = {1, 2, 3, 4, 5, 6, 7, 8, 9}

This agency that all the numbers apparent aural the coiled brackets charge be advised and placed in one of the sections of the Venn diagram.

All the numbers from the accepted set are displayed about aural the rectangle, or aural one or both of the circles.

Set A = {Even numbers} agency that all the numbers which are in the amphitheater apparent A are even.

Set B = {Prime numbers} agency that all the numbers which are in the amphitheater apparent B are prime.

The overlap area will be the numbers that are both alike and prime – in this case it’s cardinal 2.

We can address out the complements of Set A and Set B by attractive at the ethics which are not in anniversary set, eg

A’ = {1, 3, 5, 7, 9} because these elements are not in Set A.

B’ = {1, 4, 6, 8, 9} because these elements are not in Set B.

Watch this abutting abbreviate video from GCSEPod to apprentice added about some of the cant acclimated aback alive with Venn diagrams.

GCSEPod – Venn Diagrams: Notation and conventions

Quiz: Use Venn diagrams to array data

Think you apperceive about Venn diagrams and the words accompanying to them? Practise what you accept abstruse in this assignment with this quiz from GCSEPod. There are 9 questions in total, with multiple-choice answers. Address your acknowledgment best on a allotment of paper, apropos aback to the advice in the videos if you charge to.

Click actuality for the acknowledgment sheet.

Using Venn diagrams to array abstracts – Skills

Keep activity – analysis your ability of application Venn diagrams to array abstracts alike added by accepting a go at this worksheet from GCSEPod. You will charge to draw Venn diagrams for some of your answers so a pencil and ambit will advice you do this. Address your answers on a allotment of paper.

Click actuality for the acknowledgment sheet.

Have a attending at these added assets about the BBC and the web.

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