(Solved): Problems: (a) 'Nand'-sometimes written as - is the logical connective with truth table Show tha ...

Problems: (a) 'Nand'-sometimes written as $?$ - is the logical connective with truth table Show that $?P?P?P,P?Q?(P?P)?(Q?Q),$ and $P?Q?(P?Q)?(P?Q).$ Conclude that any truth table can be obtained using $?$ as the only logical connective. (b) Which of the following statements are tautologies? (1) $(P?Q)?(P?Q)$ (2) $(P?Q)?(P?Q)$ (3) $((P?Q)?(Q?R))?(R?(?P))$ (4) $(P?Q)?Q$