Propositions and equivalences Flashcards
To remember propositional statement rules
What does this symbol stand for: ∧
And
What does this symbol stand for: ∨
Or
What does this symbol stand for: ⊕
Exclusive or
What is this symbol: =>
Implies
What is this symbol: <=>
Bi-implication
In which cases is p => q false?
When p is true and q is false
What does the following expression mean: (p⇒q)∧(q⇒p)≡p⇔q
It means that (p=>q) ∧ (q=>p) and p<=>q are logically equivalent
What does it mean that two propositions are logically equivalent
It means that the two propositions has the same truth table values.
In what cases are ‘exclusive or’ expressions true and false respectively in the proposition p ⊕ q, and why?
The proposition is false if both p & q has the same truth values (T, T & F, F). This is because ‘exclusive or’ is only true when exactly one of either p or q is true
What is the name of this propositional law: p∨(q∧r)≡(p∨q)∧(p∨r) ,
p∧(q∨r)≡(p∧q)∨(p∧r)
The distributive laws
What is the name of this propositional law:
¬(p∧q)≡¬p∨¬q ,
¬(p∨q)≡¬p∧¬q
De Morgan’s laws
What are the distributive laws? (Write the logic with words)
p∨(q∧r)≡(p∨q)∧(p∨r) ,
p∧(q∨r)≡(p∧q)∨(p∧r)
p or (q and r) equivalent to (p or q) and (p or r)
RULE OF THUMB:
multiply into the parenthesis and switch the and/or
What is the name of this equivalence:
p => q ≡ ¬q => ¬p
Contraposition
How can p => q be written using only and/or/negate
¬p∨q
How can bi-implication (<=>) be written using and/or/negate and implies?
(p => q) ∧ (q => p)
