Every relation in $$3NF$$ is also in $$BCNF$$

A relation $$R$$ is in $$3NF$$ if every non-prime attribute of $$R$$ is fully functionally dependent on every key of $$R$$

Every relation in $$BCNF$$ is also in $$3NF$$

No relation can be in both $$BCNF$$ and $$3NF$$

$$\overline {bd} $$

$$\overline {bd} + \overline {bc} $$

$$\overline {bd} + a\overline {bc} d$$

$$\overline {bd} + \overline {bc} + \overline {cd} $$

$$\exists x\left( {real\left( x \right) \vee rational\left( x \right)} \right)$$

$$\forall x\left( {real\left( x \right) \to rational\left( x \right)} \right)$$

$$\exists x\left( {real\left( x \right) \wedge rational\left( x \right)} \right)$$

$$\exists x\left( {rational\left( x \right) \to real\left( x \right)} \right)$$

$$X$$

$$X+Y$$

$$X \oplus Y$$

$$Y$$