) Derive that truth table for p^q→p is a tautology MTH 211

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COURSE CODE:                     MTH 211

          COURSE TITLE:                      LOGIC AND LINEAR ALGEBRA

           CLASS:                                    ND2 CIVIL , MECHANICAL, ELECTRICAL AAND MECHANICAL          

                                                             ENGINEERING                        

  •        THE TRUTH TABLE FOR S

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 And Mariam is able to provide solution to complicated problem =Q

S = Pv Q]

PQP^QPvQPv Q]
TTFFTTT
TFFTFTT
FTTFFTF
FFTTFFT
  1.   (a) Derive that truth table for p^q→p is a tautology

SOLUTION

PQP^QPvQ
TTFFTTT
TFFTFTF
FTTFFTT
FFTTFFT
PQP^QPvQP^Q→P
TTFFTTTT
TFFTFTFT
FTTFFTTT
FFTTFFTT

CONDITIONAL STATEMENTS ARE ONLY FALSE WHEN P IS TRUE AND Q IS FALSE FOR ALL OTHER CONDITIONS IT’S TUE  

According to the definition of tautology being true any state given as the premises.

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