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

Necessary and Sufficient Conditions Lesson objectives: To be able to understand the concepts of necessary and sufficient conditions and recognise them as strengths or flaws in arguments with reference to the credibility of evidence. To be able to use necessary and sufficient conditions to make a judgement of an argument. To be able to use necessary and sufficient conditions to help construct a counter argument.

Necessary Conditions Write down several words which mean necessary (synonyms for necessary). Write a short sentence explaining what ‘necessary’ means.

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

Examples of Necessary Conditions It is necessary to have talent to become a world class sports player. It is necessary to have talent to become a world class sports player. It is necessary to qualify for the world cup to win it. It is necessary to qualify for the world cup to win it. It is necessary to be female to be pregnant. It is necessary to be female to be pregnant. It is necessary to have oxygen, fuel and ignition to make fire. It is necessary to have oxygen, fuel and ignition to make fire.

Sufficient Conditions Write down several synonyms for the word sufficient. Write a short sentence explaining what ‘sufficient’ means.

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

Sufficient Condition Being born in the UK of British parents is a sufficient condition for obtaining a British passport. This is the same as saying ‘ If you are born in Britain of British parents you can have a British passport.’ Being born in the UK of British parents is a sufficient condition for obtaining a British passport. This is the same as saying ‘ If you are born in Britain of British parents you can have a British passport.’ It is sufficient to be the eldest son of the reigning monarch to make you the heir to the throne. It is sufficient to be the eldest son of the reigning monarch to make you the heir to the throne.

Necessary and Sufficient Conditions For the following work out the relationship between X and Y. Necessary? Sufficient? Both? Neither? X = Smoking cigarettes X = Smoking cigarettes Y = Developing lung cancer Y = Developing lung cancer

Necessary and Sufficient Conditions X = Driving above the legal blood alcohol limit X = Driving above the legal blood alcohol limit Y = Being convicted of driving above the legal blood alcohol Y = Being convicted of driving above the legal blood alcohol

Necessary and Sufficient Conditions X = Having 3 A levels X = Having 3 A levels Y = Getting a place on a degree course at university Y = Getting a place on a degree course at university

Necessary and Sufficient Conditions X = Labour winning a large majority of seats in the House of Commons X = Labour winning a large majority of seats in the House of Commons Y =The labour party forming a government Y =The labour party forming a government

Necessary and Sufficient Conditions X = Having all six numbers in the National Lottery draw on a valid ticket. X = Having all six numbers in the National Lottery draw on a valid ticket. Y = Being at least one of the winners of the jackpot prize. Y = Being at least one of the winners of the jackpot prize.

Necessary and Sufficient Conditions - Answers 1 is neither 2 is necessary 3 is neither 4 is sufficient 5 is both (or is it …?)

Constructing Conditions For each of the following construct conditions that are: 1) Necessary (but not sufficient) 2) Sufficient (but not necessary) 3) Both necessary and sufficient 4) Neither 5) A counter assertion

Today is Thursday Necessary = Today is a weekday Sufficient = Today is the 18 th February 2010 Both necessary and sufficient = Yesterday was Wednesday Irrelevant = My name is Bill Counter argument = Today is Saturday

I am a Sagittarian (21 st Nov – 20 th Dec) Necessary = I was born in Nov or Dec Sufficient = I was born on 21 st Nov Both necessary and sufficient = I was born between 21 st Nov and 20 th Dec inclusive Irrelevant = Her name is Dannie Counter argument = I am an Aquarius

It is daytime Necessary = Sufficient = Both = Irrelevant = Counter argument =

I have been placed in Homework detention Necessary = Sufficient = Both = Irrelevant = Counter argument =

Being convicted of shop lifting Necessary = Sufficient = Both = Irrelevant = Counter argument =

I have achieved a grade A in critical thinking AS Necessary = Sufficient = Both = Irrelevant = Counter argument =

The War is Over Necessary = Sufficient = Both = Irrelevant = Counter argument =

Necessary and Sufficient Conditions Plenary: Review of Lesson Objectives To be able to understand the concepts of necessary and sufficient conditions and recognise them as strengths or flaws in arguments with reference to the credibility of evidence. To be able to use necessary and sufficient conditions to make a judgement of an argument. To be able to use necessary and sufficient conditions to help construct a counter argument.

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