Can you think of five famous people who you feel are rational/logical?

Deciding whether a syllogism is valid

Trying to decide if a syllogism is valid is not easy.

Venn diagrams can help (at last a good use for Venn diagrams!)

Deciding whether a syllogism is valid

• Some IB students are from Russia

• All Russians are good at drinking vodka

• Therefore some IB students are good at drinking vodka

Is this a valid argument?

Mmmmmmm…Vodka!

Using Venn diagrams

• Some IB students are from Russia

IB Students

Russians

IB Students who are Russian

Using Venn diagrams

• All Russians are good at drinking vodka

IB Students

Russians

Good vodka drinkers

Using Venn diagrams

• Therefore some IB students are good at drinking vodka

IB Students

Russians

Good vodka drinkers

Another example

• All As are Bs

• All Bs are Cs

• Therefore all Cs are As

Another example

• All As are Bs

A

B

Another example

• All Bs are Cs

A

B

C

Another example

• Therefore all Cs are As

A

B

C

These Cs are not As

The syllogism is not valid

Another example!

• All As are Bs

• Some As are Cs

• Therefore some Bs are Cs

Another example!

• All As are Bs

A

B

Another example!

• Some As are Cs

A

B

C

Another example!

• Therefore some Bs are Cs

A

B

C

The syllogism is valid

Now your turn

Using Venn diagrams in your notebooks, decide whether each of the following arguments is valid or invalid.

Valid or invalid

• All Norwegians eat hotdogs

• Edward eats hotdogs• Therefore Edward is

Norwegian

Valid or invalid

• No Swedes have red noses

• Mr Luitjens has a red nose

• Therefore Mr Luitjens is not a Swede

Valid or invalid

• All IB1 boys are brave• Some brave people

are compassionate• Some IB1 boys are

compassionate

Valid or invalid

• Some physicists are frauds• Some frauds are not wealthy• Therefore some physicists are not wealthy

Valid or invalid

• All Norwegians have dogs• No good football players have dogs• Therefore no Norwegians are good football

players

Valid or invalid

• All clever girls are red-headed

• All red heads are rich• Therefore all clever

girls are rich

Valid or invalid

• No teachers are clever

• No IB1 students are clever

• Therefore no IB1 students are teachers