# True and false statements

**Logic**Level 3

Which of the following statements are true and which are false, knowing that the entire set is uncontradictory?

S1. Statements 2 and 3 are either both true either both false.

S2. Exactly one of the statements 4 and 5 is true.

S3. Exactly one of the statements 4 and 6 is true.

S4. Exactly one of the statements 1 and 6 is true.

S5. Statements 1 and 3 are of the same type (both true or both false).

S6. Exactly one statement from statements 2 and 5 is true.

Write the answer as the concatenation of the digits 1 and 0 for the truth values of the statements (true and false) starting from S1 to S6, where for the value true corresponds 1 and for the value false corresponds 0. For example if the first 2 statements would be true and the rest false, the answer would be 110000.

If the correct answer begins with some number of leading 0s remove it from writing the answer. For example, if the answer is 001100, write 1100 anyway.