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IB MATH STUDIES

SETS, LOGIC AND PROBABILITY

LOGIC AND TRUTH TABLE SUMMARY

Propositions are represented by p : q : r: etc

Negation This means not …..

p p
T F
F T

Two propositions can be connected by logic symbols to give a new statement (proposition)

Conjunction p and q

 
p q p q
T T T
T F F
F T F
F F F
 
 

 

Disjunction p or q or both
 
 
p q p q
T T T
T F T
F T T
F F F
 
 
 
 

 

Exclusive disjunction p or q but not both
 
 
p q p q
T T F
T F T
F T T
F F F
 
 

 

Implication if p then q
 
 
p q p q
T T T
T F F
F T T
F F T
 
 
 

The compound proposition is only false when the first proposition is True and the second False.

 
Equivalence  If and only if
 
 
p q p q
T T T
T F F
F T F
F F T
 
 
       
.

p q

 

Converse is q p

   Inverse is p q
  Contrapositive is q p
       
 

Tautology: A statement that is true whatever the truth values of the original propositions.

   
 

Contradiction: A statement that is false whatever the truth values of the original propositions.

   
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