If 3SAT reduces to its complement then PH=NP In Chapter 5 of the Arora–Barak complexity theory textbook we are asked to prove the following statement:


  If 3SAT is polynomial-time reducible to its complement then PH=NP.
  How do I prove this statement?
Show that in that case $\text{NP=coNP}$ which means $\Sigma^p_1=\Pi_1^p$, so the hierarchy collapse to the first level.