$2.$ Define the logical operator $$ as NOR: p $$ q is true when both p and q are false, and otherwise it is false.

pqp$$q

TTF Truth table for $$: T F F FTF FFT

$($a$)$ Show that p $$ p is logically equivalent to $$p$.$

$($b$)$ Show that $($p $$ q$)($p $$ q$)$ is logically equivalent to p $$ q$.$

Note: these two facts, together with the result of Exercise $49$ in your book, show that $\{\}$ is a functionally complete collection of logical operators; that is$,$ you could do all of propositional logic just using $.$ See Exercises $47-58$ for more on this topic.