Consider the following entity relationship diagram $$(ERD),$$ where two entities $$E1$$ and $$E2$$ have a relation $$R$$ of cardinality $$1:m.$$

The attributes of $$E1$$ are $$A11, A12$$ and $$A13$$ where $$A11$$ is the key attribute. The attributes of $$E2$$ are $$A21, A22$$ and $$A23$$ where $$A21$$ is the key attribute and $$A23$$ is a multi-valued attribute. Relation $$R$$ does not have any attribute. A relational database containing minimum number of tables with each table satisfying the requirements of the third normal form $$(3NF)$$ is designed form the above $$ERD.$$ The minimum number of tables in the database is

Consider the partial implementation of a $$2$$-bit counter using $$T$$ flip-flops following the sequence $$0$$-$$2$$-$$3$$-$$1$$-$$0,$$ as shown below.

To complete the circuit, the input $$X$$ should be

$$SR.$$ latch made by cross coupling two $$NAND$$ gates if $$S=R=0,$$ Then it will result in

Consider a multiplexer with $$X$$ and $$Y$$ as data inputs and $$Z$$ as control input. If $$z=0$$ select input $$x,$$ and $$z=1$$ selects input $$Y$$. what are the connections required to realize the $$2-$$variable Boolean function $$f=T+R$$ without using any additional Hardware?