#1.01a
Understand and be able to use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion.
In particular, learners should use methods of proof including proof by deduction and proof by exhaustion.
#1.01b
Understand and be able to use the logical connectives \(≡\), \(\implies\), \(\iff\).
Learners should be familiar with the language associated with the logical connectives: “congruence”, “if..... then” and “if and only if” (or “iff”).
#1.01c
Be able to show disproof by counter example.
Learners should understand that this means that, given a statement of the form “if \(P(x)\) is true then \(Q(x)\) is true”, finding a single \(x\) for which \(P(x)\) is true but \(Q(x)\) is false is to offer a disproof by counter example.
Questions requiring proof will be set on content with which the learner is expected to be familiar e.g. through study of GCSE (9-1) or AS Level Mathematics.
Learners are expected to understand and be able to use terms such as “integer”, “real”, “rational” and “irrational”.
#1.01d
Understand and be able to use proof by contradiction.
In particular, learners should understand a proof of the irrationality of \(\sqrt{2}\) and the infinity of primes.
Questions requiring proof by contradiction will be set on content with which the learner is expected to be familiar e.g. through study of GCSE (9-1), AS or A Level Mathematics.