Review Excercise Continuation      <<< Back

            1.14) Show that the statements p V q V r V s  and ( p ^ q ^ r  )  s are equivalent.

                    Solution:
 
 
 

p
q
r
s
p V q V r V s
T
T
T
T
T
T
T
T
F
T
T
T
F
T
T
T
T
F
F
T
T
F
T
T
T
T
F
T
F
T
T
F
F
T
T
T
F
F
F
T
F
T
T
T
T
F
T
T
F
T
F
T
F
T
T
F
T
F
F
T
F
F
T
T
T
F
F
T
F
T
F
F
F
T
T
F
F
F
F
F

 
 
 
 
p
q
r
s
p
q
r
p^q^r  s
T
T
T
T
F
F
F
T
T
T
T
F
F
F
F
T
T
T
F
T
F
F
T
T
T
T
F
F
F
T
T
T
T
F
T
T
F
T
F
T
T
F
T
F
F
T
F
T
T
F
F
T
F
T
T
T
T
F
F
F
F
T
T
T
F
T
T
T
T
F
F
T
F
T
T
F
T
F
F
T
F
T
F
T
T
F
T
T
F
T
F
F
T
F
T
T
F
F
T
T
T
T
F
T
F
F
T
F
T
T
T
T
F
F
F
T
T
T
T
T
F
F
F
F
T
T
T
F

            The truth values for p V q V r V s & ( p ^ q ^ r  )  s are same in each case, then we can
            conclude that p V q V r V s  and  ( p ^ q ^ r  )  s are logically equivalent, written as

                                        p V q V r V s   ( p ^ q ^ r  )  s

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