Please help me with the following problem.

No, Yes, No, No.

Step-by-step explanation:

"It is not the case that x is equal to 100." This means that x ≠ 100.

"x is not equal to 300." The problem has nothing to do with 300. We know that x ≠ 100, but the fact that x ≠ 300 doesn't prove or deny anything about the statement x ≠ 100.

"x is equal to 100." This is the complete opposite of the original statement! If x = 100, then this completely denies or negates the fact that x ≠ 100.

"It is not the case that x is equal to 400." Again, 400 has nothing to do with the statement x ≠ 100, so the statement neither proves nor denies the statement x ≠ 100.

"x is equal to 300." Same story: 300 has nothing to do with x ≠ 100, so it doesn't change anything about x ≠ 100.