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  3. 1)  recall, a truth table for a proposition

1)  Recall, a truth table for a proposition involving propositional symbols p and q uses four rows...

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Advance Math

1)  Recall, a truth table for a proposition involvingpropositional symbols p and q uses four rows for the cases p true,q true, p true, q false, p false, q true and p false, q false (inthat order). For example  the outcome for p v¬q  is  T, T, F, T  since theexpression is only false when q is true but p is false. Of course,we have the same outcome for any logically equivalent propositionincluding ¬(¬p ∧ q), (¬p ∧ q) → false  and q → p. Ofthese, q → p clearly reduces the number of symbols to a bareminimum. Find \"minimal expressions\" for the other 15 possibleoutcomes, which are listed below:

a) FFFF

b) FFFT

c) FFTF

d) FFTT

e) FTFF

f) FTFT

g) FTTF

h) FTTT

i) TFFF

j) TFFT

k) TFTF

l) TFTT

m) TTFF

n) TTTF

o) TTTT

You may only use symbols from the set p, q, → , ∧ , ∨,(,  ),  ↔ ,false,  true, ¬ .  Each ofthose count 1 toward the length of the expression.(Note:  falseand true still count assingle symbols, even though they have multiple letters.) In some ofthe answers, your expression might have just p in it and not q orvice versa. Of course, there are also two answers that don't haveeither p or q in them!

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