C1-4

Question 1

what is a prime number

Answer 1

number that has exactly two positive divisors (1 and the prime number)

Question 2

what is a composite number

Answer 2

an integer greater than 1 which is not prime

Question 3

what is the smallest prime number

Answer 3

2

Question 4

definition

Answer 4

introduction of a term or concept, as unambiguous as possible

Question 5

statement

Answer 5

a sentence that is either true or false

Question 6

proof

Answer 6

a chain of logical arguments that establishes the truth of a statement

Question 7

conjecture

Answer 7

a statement that is believed to be true but has not been proved

Question 8

theorem

Answer 8

a statement which is known to be true

Question 9

proposition

Answer 9

in books on logic this is used synonymously to ‘statement’

also used for less important theorems

Question 10

lemma

Answer 10

a true statement that is used for the proof of a more important theorem

Question 11

corollary

Answer 11

a true statement that easily follows from a theorem

Question 12

principle

Answer 12

a fundamental law assumed to be true, usually without proof

Question 13

axiom

Answer 13

one of a set of statements that are assumed to be true and form the basis of a branch of maths

Question 14

direct proof

Answer 14

prove smaller implications which are obvious until the required thing is proved

Question 15

proof by contraposition

Answer 15

use the fact that
p implies q iff not q implies not p

so here lead from q being false to p being false

Question 16

Proof by contradiction

Answer 16

to prove that p is true, we assume p is false. if the assumption leads to a contradiction we can establish that p cannot be false and so must be true

Question 17

Proof by induction (eg P(n) is true)

Answer 17

base case- verify P(1) is true
induction step- assume that P(n) is true for a fixed n and use this to prove that P(n+1) is true
Conclusion- by induction principle, P(n) holds true for all integers (example)