The set $\{->,\}$ of connectives is adequate for Propositional Logic, that is$,$ every other connective

can be recast in terms of the two above. Show that by providing for every formula schema below

an equivalent schema that uses only $->,$ and the variables in the schema. Prove the equivalence

between each given schema and yours by using a truth table.

Below, A$,$ B stand for arbitrary formulas.

$1.$

$2.$A

$3.$ A $$ B

$4.$ A $$ B

$5.$ A $$ B