I have been solving problem set 0 from Harvard’s CS50 for SQL online course. There is a question in it, which says:

In 7.sql, write a SQL query to count the number of players who bat (or batted) right-handed and throw (or threw) left-handed, or vice versa.

There are two columns in the players table called bats and throws.

I tried two approaches:

SELECT COUNT(id) FROM players
WHERE (bats = 'R' AND throws = 'L') OR (bats = 'L' AND throws = 'R');

which gives the correct result.

However, I also tried this:

SELECT COUNT(id) FROM players
WHERE throws<>bats AND throws IS NOT NULL AND bats IS NOT NULL;

which (according to me) logically, should give the same answer. Can someone explain what I am missing? Sorry if there are any formatting issues as this is my first question.