I have these discrete maths notes make more than $20$ questions with solutions,"Chapter$2$:TheLogicOf CompoundStatements Sections$2\mathrm{.}1-2\mathrm{.}3$: LogicalFormsandLogical Equivalences;ConditionalStatements;Arguments De nition$1$Astatementorapropositionisasentence that istrueor falsebutNOTboth. Example:Thefollowingareexamplesofstatements: $1.2+3=10$:This isafalsestatement $2.2+3=5$isatruestatement. $3.$ "Thisclass isMTH$213".$ Example:ThefollowingareNOTstatements:$1.$ x$+$y$>0$: $2.$ "Heisacollegestudent". Astatementformisanexpressionmadeupofstatement variables suchasP; Q; Rand logical operations such as ;$^$; $\_$:Thetruthtableforagivenstatementform displays thetruthvalues thatcorrespondtoall possible combinationsoftruthvaluesfor itscompoundstatement variables. LogicalOperations: LetPandQbetwostatements.Compoundstatements canbe formedfromsimplestatementsusing logical operations $1.$ ThenegationofP:~P: It isNOTthecasethatP: P ~P $10012.$ TheConjunctionofPandQ$($PandQ$)$:P$^$Q: This statement is only true if bothP andQare true. P Q P$^$Q $1111000100003.$ The disjunction of P andQ$($Por Q$)$: P$\_$Q: This statement is true if at leastPorQare true. P Q P$\_$Q $1111010110004.$ Theconditional statement$($P impliesQ$)$:P$!$Q: Thisstatement isfalseonlyifthehypothesis istrueandtheconclusions isfalse. P Q P$!$Q $111100011001.5.$ TheBiconditional statement $($P if andonly ifQ$)$: P$Q: It is trueonly ifbothPandQhavethe samevalues. P Q P$Q $111100010001.$ Remarks: $1.$Order ofOperations: Parentheses, ; $^$;$\_($Coequal$),!$;$$($Coequal$).2.$ PbutQmeansPandQ:$3.$ NeitherPnorQmeans$($ P$)^($ Q$)$: $4.$ P$\_$QissometimesreferredtoastheinclusiveOR. The exclusiveor isP Q: It has the truth table P Q P Q $110101011000.5.$ Twostatement formsPandQare logicallyequivalent $($P Q$)$ if bothstatementshave the same truthtables. $6.($P$!$Q$)($ P$\_$Q$)$: $7.$ Atautology isa statement that is always true. A contradictionisastatementthat isalwaysfalse$\mathrm{.}8.$ DeMorgansLaws:ThenegationofANDisORand thenegationofORisAND. $9.$ SeeTheorem$2\mathrm{.}1\mathrm{.}1$ inpage$35$ inthe textbook for LogicalEquivalences. Noticethat t isusedfor true $($tautology$)$andcisusedfor false$($contradiction$)$ Example:Constructthetruthtablefor P$^($Q$!$R$)$: Solution: Thenumberof rows inatruthtable isalways equalsto$2($#distinctvariables$)$:Hence,weneed$8$rows in thetruthtable. P Q R P Q$!$R P$^($Q$!$R$)111010110000101010100010011111010100001111000111"$