Answer :
If A and B are independent, then [tex]P(A\cap B)=P(A)P(B)[/tex].
a.
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=P(A)+P(B)-P(A)P(B)[/tex]
[tex]P(A\cup B)=0.5+0.2-0.5\cdot0.2[/tex]
[tex]\boxed{P(A\cup B)=0.6}[/tex]
b. I'm guessing the ? is supposed to stand for intersection. We can use DeMorgan's law for complements here:
[tex]P(A^c\cap B^c)=P(A\cup B)^c=1-P(A\cup B)[/tex]
[tex]P(A^c\cap B^c)=1-0.6[/tex]
[tex]\boxed{P(A^c\cap B^c)=0.4}[/tex]
c. DeMorgan's law can be used here too:
[tex]P(A^c\cup B^c)=P(A\cap B)^c=1-P(A\cap B)=1-P(A)P(B)[/tex]
[tex]P(A^c\cup B^c)=1-0.5\cdot0.2[/tex]
[tex]\boxed{P(A^c\cup B^c)=0.9}[/tex]