Discrete Mathematics Session 3

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Complete the truth table for “exclusive or.”

 

p

q

p w q

p v q

~( p v q)

(p w q) v ~( p v q)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(p w q) v ~( p v q) may be abbreviated p XOR q or as p ¿ q

 

Logical Equivalence

 

Two statement forms are called logically equivalent if, and only if, they have identical truth values for each possible substitution for their statement variables.  Logical equivalence of p and q is denoted by p /q.

 

Show that -(p ¸ q) / -p º -q

 

p

q

~p

~q

p Λ q

~(p Λ q)

~p V ~q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Complete a truth table for p Λ ~ p

 

Complete a truth table for [(p Λ ~q) V ~p] V q

 

Tautology

 

Contradiction

 

Table of Logical Equivalences (p. 14)

 

Show that (p Λ q) Λ  (p Λ ~q) / c

 

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