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Table1080Solutionoftheexample
p
0
0
0
0
1
1
1
1
q
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
r
p∨q
0
0
1
1
1
1
1
1
Weproceedsimilarlywiththeformulaep⇔randq∧r.Justremembertoread
thevaluesoftheirelementsfromappropriatecolumns.Letusconsiderfor
instancetherow4(pisfalse,qandraretrue).Insuchacasethevalueofp⇔r
is0(thevalueofpis0,thevalueofris1,sotheyaredifferent),andthevalueof
q∧ris1(bothqandraretrue,soitfollowsfromtheTable1.2thattheir
conjunctionisalsotrue).TheresultsarelistedintheTable1.9.
Table1090Solutionoftheexample
p
0
0
0
0
1
1
1
1
q
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
r
p∨q
0
0
1
1
1
1
1
1
p⇔r
1
0
1
0
0
1
0
1
q∧r
0
0
0
1
0
0
0
1
Thenextstepisevaluatingtheleftsideoftheinvestigatedformula,i.e.
(p∨q)∧(p⇔r).AgainweusethecontentsoftheTable1.2,bearinginmind
thatthecalculationsusethelogicalvaluesoftheexpressions(p∨q)
and(p⇔r).Forexample,inthefirstrow(p∨q)hasvalue0,while(p⇔r)has
value1,sothevalueoftheirconjunctionwillbe0.Theresultsarepresentedin
theTable1.10.
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