DeMorgan's Laws
DeMorgan's Laws are used to negate these types of compound statements
What are conjunctions and disjunctions?
The law illustrated below:
P1: h ->m
P2: h
C: m
What is the law of detachment?
The law illustrated below:
P1: w V r
P2: ~r
C: w
What is the law of disjunctive inference?
P1: w V p
P2: p
C: ~w
What is Invalid?
Find the logically equivalent statement.
~(p ∧ q) ≡
~(p ∧ q) ≡ ~p ∨ ~q
The law illustrated below:
P1: ~k ^ v
C: ~k
What is the law of simplification?
The law illustrated below:
P1: ~u -> r
P2: ~r
C: u
What is the law of contrapositive inference?
P1: It's cold or it's not winter.
P2: It's not cold.
C: It's not winter.
What is Valid?
Find the logically equivalent statement:
~(p V ~ q) ≡
~(p V ~ q) ≡ ~p ^ q
The law illustrated below:
P1: p
C: p v q
What is the law of addition?
The law illustrated below:
P1: z -> ~p
P2: ~p -> d
C: z -> d
What is the Chain Rule?
P1: If I don't charge my phone, then it will die.
P2: My phone died.
C: I didn't charged my phone.
Invalid
Find the logically equivalent statement:
~[(~k V~ s)^(f V b)] ≡
~[(~k V~ s)^(f V b)] ≡ (k ^ s)V(~f ^ ~b)
The law illustrated below:
P1: Sally is tired only if she didn't go to bed early.
C: If Sally went to bed early, then she isn't tired.
What is the law of contrapositive?
The law illustrated below:
P1: No pigs can fly.
P2: Babe can fly.
C: Babe is not a pig.
What is the law of contrapositive inference?
P1: It's a kee if it's a dee.
P2: It's not a kee.
C: It's not a dee.
What is Valid?
True or False?
p -> ~q ≡ ~(p ^ q)
True
p -> ~q ≡ ~p V ~q
The laws illustrated below:
P1: ~m -> p
P2: ~p ^ r
C: m
What are the laws of simplification and contrapositive inference?
The laws illustrated below:
P1: (r ^ q) V w
P2: ~r V ~q
C: w
What are DeMorgan's law and the law of disjunctive inference?
P1: All bops are pops.
P2: Sop is a pop.
C: Sop is a bop.
What is invalid?