Solution to Translate the following statements into symbolic form using capital letters to represent affirmative Identify the … - Sikademy
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Archangel Macsika

Translate the following statements into symbolic form using capital letters to represent affirmative Identify the main operator in the following propositions: ~[~(P & ~Q)] & ~(R –>~S) ~[~L v ~(J –> ~M)] ~[(H & ~L) & ~B] –> ~(~Y & ~K) ~[~(~F v J) v (~M v ~E)] & ~(~C & ~L)

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~[~(P & ~Q)] & ~(R –>~S)

\iff~[[~(P & ~Q)] v (R –>~S)]

\iff ~[~(P & ~Q) v (~R v~S)] (Using DeMorgan's laws in each step)

\iff ~[~(P & ~Q) v ~(R & S)]

\iff (P & ~Q) & (R & S)

\iff P & ~Q & R & S


~[~L v ~(J –> ~M)]

\iff ~[~L v ~(~J v ~M)]

\iff ~[~L v (J & M)]

\iff ~[(~L v J) & (~L v M)] (Using DeMorgan's laws in each step)

\iff ~[(L->J) & (L->M)] (Using definition of p \to q \iff \lnot p v q )

\iff ~(L->J) v ~(L->M)


~[(H & ~L) & ~B] –> ~(~Y & ~K)

\iff (~Y & ~K) –> [(H & ~L) & ~B] (Using p \to q \iff \lnot q \to \lnot p )

\iff (~Y & ~K) –> [~(~H v L) & ~B] (Using DeMorgan's laws in each step)

\iff ~(Y v K) –> ~[(~H v L) v B]

\iff [(~H v L) v B] -> (Y v K) (Using p \to q \iff \lnot q \to \lnot p )

\iff [(H -> L) v B] -> (Y v K) (Using definition of p \to q \iff \lnot p v q )


~[~(~F v J) v (~M v ~E)] & ~(~C & ~L)

\iff [ (~F v J) & ~(~M v ~E)] & (C v L) (Using DeMorgan's laws in each step)

\iff [ (~F v J) & (M & E)] & (C v L)

\iff [ (F -> J) & (M & E)] & (C v L) (Using definition of p \to q \iff \lnot p v q)


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Question ID: mtid-5-stid-8-sqid-3992-qpid-2691