Chapter 9

Logic

Problem

Three dogs called Lassie, Timmy and Fido have either black, brown or tri-colour hair. The dogs have lived with their owners for either 9 months, 2 years or 7 years.• The dog who has lived with their owner the longest has brown

hair.• Fido has lived with his owner for longer than Lassie.• Fido does not have tri-colour hair and Lassie does not have black

hair.How long has each dog lived with its owner and what colour hair does it have?

Inductive and deductive logic

All students in this class are studying maths studies.

Alix is in this class.

Therefore Alix is studying maths studies.

All students observed entering the maths studies class are girls.

Therefore, all maths studies students are girls.

Deductive Logic Inductive Logic

Which is better?

TOK

Truth table

These are the two original propositions and the different combinations of ‘true’ and ‘false’ possible.

This is the negation of p, so it’s the opposite of whatever is in p.

This is the conjunction (intersection) of p and q. It is true only when both p and q are true.

This is the disjunction (union). It is true unless both both p and q are false.

This is the exclusive disjunction, which means it is one or the other but not both.

This is an implication, ‘p implies q’. It is true whenever p is false or when both p and q are true.

This is equivalence. It is true when either both propositions are false or both are true.