contestada

Use the laws of propositional logic to prove that each statement is a tautology. (p n q) rightarrow (p V r) p rightarrow (r rightarrow p) (8 points each for a total of 16, zyBook section 1.5, exercise 1.5.3(a, b))

Respuesta :

Answer:

See explanation below.

Explanation:

If the statement is a tautology is true for all the possible combinations

Part a

[tex] (p \land q) \Rightarrow (p \lor r)[/tex] lets call this condition (1)

[tex](p \land q) [/tex] condition (2) and [tex](p \lor r)[/tex] condition (3)

We can create a table like this one:

p       q     r      (2)       (3)     (1)  

T       T     T      T        T       T

T       T     F      T        T       T        

T       F     T      F        T       T

T       F     F      F        T       T

F       T     T      F        T       T

F       T     F      F        F       T

F       F     T      F        T       T

F       F     F      F        F       T

So as we can see we have a tautology.

Part b

[tex] p \Rightarrow (r \Rightarrow p)[/tex] lt's call this condition 1

And [tex] (r \Rightarrow p)[/tex] condition 2

We can create the following table:

p     r       (2)     (1)

T     T       T       T

T     F       T       T

F     T       F       T

F     F       T       T

So is also a tautology.

Otras preguntas