Necessary and Sufficient Conditions Jan 2007 Updated March 2007; July 2010

Necessary and Sufficient Necessary and Sufficient ConditionsConditions

Jan 2007Jan 2007

Updated March 2007; July 2010Updated March 2007; July 2010

Necessary and Sufficient Necessary and Sufficient ConditionsConditionsLesson objectives:Lesson objectives:

To be able to understand the concepts of necessary To be able to understand the concepts of necessary and sufficient conditions and recognise them as and sufficient conditions and recognise them as strengths or flaws in arguments with reference to the strengths or flaws in arguments with reference to the credibility of evidence.credibility of evidence.

To be able to use necessary and sufficient conditions to To be able to use necessary and sufficient conditions to make a judgement of an argument.make a judgement of an argument.

To be able to use necessary and sufficient conditions to To be able to use necessary and sufficient conditions to help construct a counter argument.help construct a counter argument.

Necessary ConditionsNecessary Conditions

Write down several words which mean Write down several words which mean necessary (synonyms for necessary).necessary (synonyms for necessary).

Write a short sentence explaining what Write a short sentence explaining what ‘necessary’ means.‘necessary’ means.

Necessary ConditionNecessary Condition

A necessary condition is A necessary condition is something which must something which must happen for something else to happen for something else to happen.happen.

Examples of Necessary Examples of Necessary ConditionsConditions

• It is necessary to have talent to It is necessary to have talent to become a world class sports player.become a world class sports player.

• It is necessary to qualify for the world It is necessary to qualify for the world cup to win it.cup to win it.

• It is necessary to be female to be It is necessary to be female to be pregnant.pregnant.

• It is necessary to have oxygen, fuel It is necessary to have oxygen, fuel and ignition to make fire.and ignition to make fire.

Sufficient ConditionsSufficient Conditions

Write down several synonyms for the Write down several synonyms for the word sufficient.word sufficient.

Write a short sentence explaining what Write a short sentence explaining what ‘sufficient’ means.‘sufficient’ means.

Sufficient ConditionSufficient Condition

A sufficient condition is A sufficient condition is something which must something which must happen to be certain that happen to be certain that something else will happen.something else will happen.

Sufficient ConditionSufficient Condition

• Being born in the UK of British parents is a Being born in the UK of British parents is a sufficient condition for obtaining a British sufficient condition for obtaining a British passport. This is the same as saying ‘ If passport. This is the same as saying ‘ If you are born in Britain of British parents you are born in Britain of British parents you can have a British passport.’you can have a British passport.’

• It is sufficient to be the eldest son of the It is sufficient to be the eldest son of the reigning monarch to make you the heir to reigning monarch to make you the heir to the throne.the throne.


For the following work out the For the following work out the relationship between X and Y.relationship between X and Y.

Necessary? Sufficient? Both? Neither?Necessary? Sufficient? Both? Neither?

• X = Smoking cigarettesX = Smoking cigarettes

• Y = Developing lung cancerY = Developing lung cancer


• X = Driving above the legal blood X = Driving above the legal blood alcohol limitalcohol limit

• Y = Being convicted of driving above Y = Being convicted of driving above the legal blood alcoholthe legal blood alcohol


• X = Having 3 A levelsX = Having 3 A levels

• Y = Getting a place on a degree Y = Getting a place on a degree course at universitycourse at university


• X = Labour winning a large majority X = Labour winning a large majority of seats in the House of Commonsof seats in the House of Commons

• Y =The labour party forming a Y =The labour party forming a governmentgovernment


• X = Having all six numbers in the X = Having all six numbers in the National Lottery draw on a valid ticket.National Lottery draw on a valid ticket.

• Y = Being at least one of the winners Y = Being at least one of the winners of the jackpot prize.of the jackpot prize.

Necessary and Sufficient Necessary and Sufficient Conditions - AnswersConditions - Answers

1 is neither1 is neither

2 is necessary2 is necessary

3 is neither3 is neither

4 is sufficient4 is sufficient

5 is both (or is it …?)5 is both (or is it …?)

Constructing ConditionsConstructing Conditions

For each of the following construct For each of the following construct conditions that are:conditions that are:

1)1) Necessary (but not sufficient)Necessary (but not sufficient)

2)2) Sufficient (but not necessary)Sufficient (but not necessary)

3)3) Both necessary and sufficientBoth necessary and sufficient

4)4) NeitherNeither

5)5) A counter assertionA counter assertion

Today is ThursdayToday is Thursday

Necessary = Today is a weekdayNecessary = Today is a weekday

Sufficient = Today is the 18Sufficient = Today is the 18thth February February 20102010

Both necessary and sufficient = Both necessary and sufficient = Yesterday was WednesdayYesterday was Wednesday

Irrelevant = My name is BillIrrelevant = My name is Bill

Counter argument = Today is SaturdayCounter argument = Today is Saturday

I am a SagittarianI am a Sagittarian(21(21stst Nov – 20 Nov – 20thth Dec) Dec)

Necessary = I was born in Nov or DecNecessary = I was born in Nov or Dec

Sufficient = I was born on 21Sufficient = I was born on 21stst Nov Nov

Both necessary and sufficient = I was Both necessary and sufficient = I was born between 21born between 21stst Nov and 20 Nov and 20thth Dec Dec inclusiveinclusive

Irrelevant = Her name is DannieIrrelevant = Her name is Dannie

Counter argument = I am an AquariusCounter argument = I am an Aquarius

It is daytimeIt is daytime

Necessary = Necessary =

Sufficient = Sufficient =

Both = Both =

Irrelevant = Irrelevant =

Counter argument =Counter argument =

I have been placed inI have been placed inHomework detentionHomework detention



Both = Both =



Being convicted of shop Being convicted of shop liftinglifting



Both = Both =



I have achieved a grade A in I have achieved a grade A in critical thinking AScritical thinking AS



Both = Both =



The War is OverThe War is Over



Both = Both =



Necessary and Sufficient Necessary and Sufficient ConditionsConditionsPlenary: Review of Lesson ObjectivesPlenary: Review of Lesson Objectives

To be able to understand the concepts of necessary To be able to understand the concepts of necessary and sufficient conditions and recognise them as and sufficient conditions and recognise them as strengths or flaws in arguments with reference to the strengths or flaws in arguments with reference to the credibility of evidence.credibility of evidence.

To be able to use necessary and sufficient conditions to To be able to use necessary and sufficient conditions to make a judgement of an argument.make a judgement of an argument.

To be able to use necessary and sufficient conditions to To be able to use necessary and sufficient conditions to help construct a counter argument.help construct a counter argument.


Jan 2007Jan 2007

Updated March 2007; July 2010Updated March 2007; July 2010

Documents

Necessary and Sufficient Conditions Jan 2007 Updated March 2007; July 2010