Find the complement of Y(a,b)=ab’+a’b, and prove that Y+Y'=1. Give a reason for each step.

what is the funciton of the circut? Write answer in minimized sum of products (SOP) form. example: Y=A'B+C

Use the pumping lemma to prove the following language is nonregular:L = {anb3n} = {abbb, aabbbbbb, aaabbbbbbbbb, …}

A Boolean function F (A,B,C) of truth table at below（PLS step by step） 1，Provide the minterm expansion of F .  2，Provide the minterm expansion and the maxterm expansion of F’s complement, respectively. Assume that we don’t care the value of F when ABC=001. i. What is the minterm expansion of F?  ii. Choose a proper value for the don’t care term and provide the shortest possible expression of POS (product of sum) for F . (Hint: Minimize the number of maxterms)