Statement 1$\Rightarrow$$\mathbf{If\: R\: is\: in\: 3NF,\: It \: is\; also\; in\: BCNF}$
$\Rightarrow$If it is in 3NF,then it is no doubt in 2NF$\Rightarrow$It does not have partial dependency.
$\Rightarrow$It won't contain Partial Dependency i.e
A functional dependency X → Y is a partial dependency if some attribute A ε X can be removed from X and the dependency still holds; that is, for some A ε X, (X – {A}) → Y.
relation Prime Attribute$\rightarrow$Non Prime Attribute.so it won't contain Prime Attribute$\rightarrow$Prime Attribute.It may contain Prime Attribute$\rightarrow$Prime Attribute.
$\Rightarrow$It won't contain Transitive dependency i.e it won't contain relation Non Key$\rightarrow$Non key.But it may contain relation Prime Attribute$\rightarrow$Prime Attribute.
Now BCNF says that if it has Functional dependency X$\rightarrow$Y,X must be a superkey.
But in Relation Prime Attribute$\rightarrow$Prime Attribute,prime Attribute is not a super key,Makes Statement1 False .
Statement 2$\Rightarrow$R may be in BCNF
$\Rightarrow$If Relation contains Prime Attribute$\rightarrow$Prime Attribute,then it is not in BCNF.
if it won't contain this relation ,it will be in BCNF,so it may/may not be in BCNF.