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LOGIC MAIN PAGE

LOGICAL OPERATORS

Sample sentences
AND operator
IF/THEN operator
NOT operator
OR operator
XOR operator

RULES OF LOGIC

Chain Rule
Conjunctive Addition
Contrapositive
DeMorgan's Law
Disjunctive Addition
Disjunctive Inference
Disjunctive Infer. (XOR)
Double Negation
Modus Ponens
Modus Tollens
Mutual Exclusion
Simplification

VALIDITY PROOFS

2-step
3-step
4-step
5-step or more
Bad Argument

Simplification

Simplification is a rule of inference pertaining to the AND operator.

Simplification means that in a given conjunction, any conjunct can be separated out and is true.

Imagine we are given the following conjunction: "Negotiations failed and war was declared." Let's recognize two distinct conjuncts in that sentence: 1) Negotiations failed, and 2) War was declared. If we are told that the entire conjunction is true, we have to conclude that each of the conjuncts must also be true. In other words, the statement "negotiations failed" is true, and the statement "war was declared" is true as well. Formally, we would write:

p ^ q: "Negotiations failed and war was declared."
----------
p: "Negotiations failed."
q: "War was declared."

The given conjunction p ^ q is above the line of dashes, and the conclusions p and q obtained by applying the Simplification rule are below the line.

 

Other examples of Simplification

A ^ B: "The book was interesting and the movie was boring."
----------
A: "THe book was interesting."
B: "The movie was boring."

 

~Y ^ X: "It's not windy and it's humid."
----------
~Y: "It's not windy."
X: "It's humid."

 

Links to Relevant Problems

These are links to validity proof problems whose solutions contain Simplification.

2-step problem
3-step problem (A)
3-step problem (B)
4-step problem
5-step problem (A)
5-step problem (B)