Consider the following queries:

$1.$ SELECT $*$ FROM invoice

WHERE customer$\_$id IN

$($SELECT customer$\_$id FROM customer

WHERE first$\_$name like $\text{'}$J$\%\text{'})$;

$2.$ SELECT invoice.$*$ FROM invoice

INNER JOIN customer

ON customer.customer$\_$id $=$ invoice.customer$\_$id

WHERE first$\_$name like $\text{'}$J$\%\text{'}$;

Which of these would be the most efficient?

a$.)$

Query #$2$ would be more efficient, as it is based on the primary key and foreign keys.

b$.)$

Query #$1$ would be more efficient, as it is based on the primary key and foreign keys.

c$.)$

Both would be the same, as both use the same indices for the join and filter.

d$.)$

Query #$2$ would be more efficient, as it is not using indexed columns.