) 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]

P	Q			P^Q	PvQ	Pv Q]
T	T	F	F	T	T	T
T	F	F	T	F	T	T
F	T	T	F	F	T	F
F	F	T	T	F	F	T

1.   (a) Derive that truth table for p^q→p is a tautology

SOLUTION

P	Q			P^Q	PvQ
T	T	F	F	T	T	T
T	F	F	T	F	T	F
F	T	T	F	F	T	T
F	F	T	T	F	F	T

P	Q			P^Q	PvQ		P^Q→P
T	T	F	F	T	T	T	T
T	F	F	T	F	T	F	T
F	T	T	F	F	T	T	T
F	F	T	T	F	F	T	T

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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