Relativization and diagonalization

$($a$)$ Statement: If NPTQBF $$ NPSPACE then NP $$ PSAT $.$

Is the statement true?

Circle the answer: yes no

$($b$)$ Statement: If A is PSPACE$-$complete then PSPACE $$ PA Is the statement true?

Circle the answer: yes no

$($c$)$ Statement: If P $=$ NP then P$=$ NP$\backslash$Sigma $.$

Is the statement true?

Circle the answer: yes no

$$ Statement: If P$\backslash$Sigma $=$ NP$$ then P $=$ NP$.$

Is the statement true?

Circle the answer: yes no