The second hypothesis is false and the third hypothesis is true.

The fourth hypothesis is true and the sixth is false.

The fourth hypothesis is false, and the fifth hypothesis is true.

The second and sixth hypotheses are both true.

The first hypothesis is true and the second is false.

The fourth hypothesis is false and the fifth hypothesis is true.

At least one of these hypotheses is true.

Question: Which hypotheses are false?

Real: 1, 3, 5, 6

False: 2, 4

Explanation:

To determine which hypotheses are true or false, let’s evaluate the consistency of each hypothesis:

Hypothesis 1: If this is true, then the second hypothesis is false and the third hypothesis is true. This creates constraints on the truth values of the other hypotheses.

Hypothesis 2: If this is true, then the fourth hypothesis is true and the sixth is false. But this conflicts with the consistency of the other hypotheses.

Hypothesis 3: If this is true, then the fourth hypothesis is false, and the fifth hypothesis is true. This means the fourth hypothesis must be false and aligns with the fifth hypothesis being true.

Hypothesis 4: If this is true, then the second and sixth hypotheses are true. This conflicts with the consistency of the hypotheses evaluated.

Hypothesis 5: If this is true, then the first hypothesis is true and the second is false. This aligns with the findings from hypothesis 1 being true and hypothesis 2 being false.

Hypothesis 6: If this is true, then the fourth hypothesis is false and the fifth hypothesis is true, which aligns with our previous findings.

Based on these evaluations, hypotheses 2 and 4 are inconsistent with the consistent set of true hypotheses.