Propositional Logic Flashcards
Define discrete mathematics
The part of mathematics devoted to the study of discrete (as opposed to continuous objects)
Define propositions
Propositions is a declarative sentence that is either true or false
Give an example of a proposition
“the moon is made out of cheese” (false)
1+0 = 1 (true)
0+0 = 2 (false)
What are the atomic proposition variables
p, q, r, s …
What are the atomic proposition constants
T(true), F (false)
Show a negative proposition
¬p
Show a conjunction
p ∧ q
Show a disjunction
p ∨ q
Show an implication
p → q
Show a bioconditional
p ↔ q
What does this symbol mean ∨
or
What does this symbol mean ∧
and
What does this symbol mean ↔
either not both / if and only i f
What does this symbol mean –>
If, then
When is a conjunction true
For a conjunction to be true both propositions must be true
When is a disjunction true
For a disjunction to be true either proposition must be true
How do you recognise a conjunction symbol
thing of construction as its similar to a roof of a house
How do you recognise a disjunction symbol
a v symbol, think of Destruction
When is a conjunction true
only when both propositions are true
When is a disjunction true
it is true if it contains a true proposition
When is an exclusive true
an exclusive is true when the propositions are different and not the same
What does an implication do
creates a conditional statement
What is the symbol for an implication
→ (an arrow pointing right)
What does the proposition on the left of the arrow stand for
the hypothesis
What does the proposition on the right of the arrow stand for
conclusion
When does the implication give a true result
both when the hypothesis is same as conclusion, but if hypothesis is false the p->q is always true
State what is a tautology
A proposition that is always true
State what is a contradiction
A proposition that is always false
State what is a contingency
A proposition that is neither a tautology nor a contradiction
