Propositional Logic and Set Notation Flashcards
What is the meaning of ‘P ⇒ Q’?
P implies Q
or
If P then Q
When is ‘P∧Q’ true?
Only when BOTH P AND Q are true
When is ‘P∨Q’ true?
When either P OR Q are true
What does the symbol ‘¬’ mean?
Negation
turns true false and vice versa
What is the meaning of ‘P⇔ Q’?
P if and only if Q
or
P is sufficient and necessary for Q
What is a tautology?
A statement that is always true
What is the converse of ‘P ⇒ Q’?
Q⇒P
What is the meaning of ‘∀’?
For all…
What is the meaning of ‘∃’?
There exists…
What is the meaning of ‘∃!’?
There exists only 1…
What is the contrapositive of ‘P ⇒ Q’?
‘¬Q⇒¬P’
Not P implies not Q
What can be said about a statement based on its contrapositive?
A statement is true, if and only if, its contrapositive is true.
Explain the set denoted by ℕ
Natural numbers
aka the counting numbers
{1,2,3,4,5,6……}
Explain the set denoted by ℤ
Integers
{….-4,-3,-2,-1,0,1,2,3,4….}
Explain the set denoted by ℚ
Rational numbers
set of a/b, where a is an integer, and b is natural
Name the set denoted by ℝ
Real Numbers
Name the set denoted by ℂ
Complex numbers
What is the meaning of the interval notation
(a,b) or ]a,b[
Open interval from a to b, not including a or b
What is the meaning of the interval notation
[a,b]
Closed interval from a to b, including a and b
What is the meaning of the interval notation
[a,b[
‘Clopen’ interval, including a but not b
What is the meaning of builder notation,
{x : P(x)} ?
The set of x, subject to some condition P(x)
What does A∩B mean? And how can it be expressed in builder notation?
A intersection B
{x : x∈A ∧ x∈B}
What does A∪B mean? And how can it be expressed in builder notation?
A union B
{x : x∈A ∨ x∈B}
What does A\B mean? And how can it be expressed in builder notation?
{x : x∈A ∧ x∉B}
What does A⊂B mean? And how can it be expressed?
A is a subset of B or A is contained in B
x∈A ⇒ x∈B
What is the meaning of A^c ?
Complement A, not A
What is the cartesian product (AxB)of two sets A, B?
AxB= {(a,b): a∈A, b∈B}
