Normal forms

Give a DNF expressing the following truth function.

ABCt$(A,B,C)$

T T T T

T TFT

TFTT

TFFF

FTTF

FTFT

FFTT

FFFT

$($Remember to put in all necessary parentheses!$)$

p$1$ A

Give a DNF expressing the truth function.

PS$12\mathrm{.}5$

$($The standard method will produce a long sentence: $6$ disjuncts, with $3$ conjuncts each. But you can cut that down to $4$

easily if you understand why the standard method works. E$.$g$.,$ instead of three disjuncts that are each true in one one

of the first three lines, find a simpler sentence that is true in all and only the first three lines.$)$

Now find a sentence expressing $t$ that involves only $A,B,C,$not,${?}^{{?}^{?}},V$ and at most $6$ occurrences of these connectives

total.

PSin