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