Let k $>1$ be an integer. Recall that k$-$SAT takes as input a boolean function in CNF such that each clause has at most k literals, and returns an assignment of the variables that

evaluates to true, and returns false otherwise. Which of the following is known to be true for all integer values of k $>1?$

There is a reduction from $2024-$SAT to k$-$SAT.

There is a reduction from k$-$SAT to $2-$SAT.

k$-$SAT is known to be NP$-$hard.

If one finds a polynomial time algorithm to solve k$-$SAT for an integer value of k $>1,$ one can conclude that P$=$NP$.$