solution.

Task $1.$ Truth Tables and Logical Equivalencies $[10$ points$]$

If $p$ and $q$ are propositions, then we can define $po+q$ as the statement $(p^{{?}^{?}}$notq$)vv(not{p}^{{?}^{?}}q).$ In

other words, $po+q$ is true if and only if $p$ is true and $q$ is false, or $p$ is false and $q$ is true. The

connective $o+$ stands for Exclusive OR or XOR.

Write the truth table of $o+,$ resorting to its definition provided above. Indicate how you

derive the resulting $o+-$column by additional columns.

Is $o+$ an idempotent connective? In other words, is the following logical equivalence

$po+p-=p$ true?

Prove that $o+$ is an associative connective, in other words show that $(po+q)o+r-=po+(qo+r).$

Use logical equivalence rules to show that notpvv$(p^{{?}^{?}}$notq$)q-=(p^{{?}^{?}}q)vvq.$