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)
~[[~(P & ~Q)] v (R –>~S)]
~[~(P & ~Q) v (~R v~S)] (Using DeMorgan's laws in each step)
~[~(P & ~Q) v ~(R & S)]
(P & ~Q) & (R & S)
P & ~Q & R & S
~[~L v ~(J –> ~M)]
~[~L v ~(~J v ~M)]
~[~L v (J & M)]
~[(~L v J) & (~L v M)] (Using DeMorgan's laws in each step)
~[(L->J) & (L->M)] (Using definition of )
~(L->J) v ~(L->M)
~[(H & ~L) & ~B] –> ~(~Y & ~K)
(~Y & ~K) –> [(H & ~L) & ~B] (Using )
(~Y & ~K) –> [~(~H v L) & ~B] (Using DeMorgan's laws in each step)
~(Y v K) –> ~[(~H v L) v B]
[(~H v L) v B] -> (Y v K) (Using )
[(H -> L) v B] -> (Y v K) (Using definition of )
~[~(~F v J) v (~M v ~E)] & ~(~C & ~L)
[ (~F v J) & ~(~M v ~E)] & (C v L) (Using DeMorgan's laws in each step)
[ (~F v J) & (M & E)] & (C v L)
[ (F -> J) & (M & E)] & (C v L) (Using definition of )