CST 329 - Week 4

This was our fourth week in CST 329 - Reasoning with Logic

Chapter 8: Reductio ad Absurdum

Reductio ad Absurdum: Often called an "indirect proof" or "indirect derivation". Similar to a subproof, but our assumption is the opposite of the conclusion we want to reach, and we create a contradiction within the indirect proof itself.
 
Basic structure of an Indirect Proof

 

An Indirect Proof

We assume that ¬¬P,

we arrive at both R and ¬R,

we conclude that the assumption must be false, so ¬P. 

 
A second example of an Indirect Proof

Contradictory Sentence: A sentence that must be false.

Chapter 9: "... if and only if...", Using Theorems

↔: The symbol for a biconditional, (Φ↔Ψ). A biconditional is true if both or neither of its contituents is true, and false otherwise.
 
Truth Table for a Biconditional
 
 
Equivalence
 
Bicondition
 
 
Many proofs for biconditionals look like the image above, with multiple subproofs
 
Proof using biconditionals and mutliple subproofs
 
 
 
Proof for a biconditional using an indirect proof
 
 Contingent Sentence: A sentence that might be true, or might be false.
 
Theorems
 
Once a theorem is proven, we can use it in any proof.
 
 
 

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