Mathematical Induction and Logic - Linear Algebra Advanced

lecture s
Mathematical induction and
logic
2.1 some useful notation from logic

2.1.1 Propositions
Aproposition is a statement that is either true or false.




2.1.2 Operations on
propositions (connectives)

Given p and
a are propositions
the conjunction of p and 9 is denoted prq (p and q)
the disjunction of
p and
a
is denoted pra (por 9)


The truth table

conjunction disjunction implication equivalence


P 9 P1q Pvqp 9 =
Pc> 9
=




TT T T I I


T F F T F F

F I F I T T


F F F F T F




An equivalence is written as
p (> 9

the negation of a proposition p is denoted ip /or -p)



Two statements and are logically equivalentif p is true precisely
p a
when a is true, denoted as p
=
a

(P 9) =
=
2pv q

P 9 -P p 9 =
-pv q (p q) =)(Tprq)
=>




T T F T T I


T F F F F I


F I T T T T


F T T
-
F T I