Statement 1 is incorrect. The statement "We go for a picnic but not for trekking" does not falsify the claim because it still supports the possibility of one of the activities happening, which aligns with the original statement.

Statement 2 is incorrect. The statement "Activities such as picnic and trekking are encouraged by the health authorities" is irrelevant to the original claim. It does not address whether one of the activities will happen or not.

Statement 3 is incorrect. The statement "We go for trekking and not for picnic" does not falsify the claim because it still supports the idea that one of the activities is taking place, which is in line with the original statement.

Statement 4 is correct. The statement "We do not go either for picnic or for trekking" directly contradicts the original claim, as it asserts that neither activity occurs, whereas the original statement claims that one of the two activities will take place.