﻿ Volko Test of Deductive Reasoning

Volko Test of Deductive Reasoning

Note: In this quiz, the word "or" always has inclusive meaning. That means, "A or B" is always equivalent to "either A or B or both of them".

Check all valid conclusions and do not check the invalid ones.

1. There is at least one A. All A are B, and at least one, but not all B are C.

All A are C.
Not all A are C.
All B are C.
Not all B are C.
All C are B.
Not all C are B.
All C are A.
Not all C are A.
All B are A.
Not all B are A.
At least one C is B.
No C is B.
At least one C is A.
No C is A.
At least one B is A.
No B is A.
At least one A is B.
No A is B.
At least one A is C.
No A is C.
All B except those that are C are A.
Not all B except those that are C are A.

2. Z is an element of the sets A and B. Y is an element of the sets A and C. X is an element of the sets B and C.

Z is an element of the set A.
Z is not an element of the set A.
Z is an element of the set B.
Z is not an element of the set B.
Z is an element of the set C.
Z is not an element of the set C.
X and Y are elements of the set A.
At least one of the two, X and Y, is not an element of the set A.
X and Y are elements of the set B.
At least one of the two, X and Y, is not an element of the set B.
X and Y are elements of the set C.
At least one of the two, X and Y, is not an element of the set C.
Y is not an element of the set A.
Y is an element of the set A.
Y is not an element of the set B.
Y is an element of the set B.
Y is not an element of the set C.
Y is an element of the set C.
Y is an element of the set A or of the set B.
Y is neither an element of the set A nor of the set B.
Y is an element of the set A, but not of the set B.
Y is an element of the set B or it is not an element of the set A.

3. P is true if and only if both Q and R are true.

If Q is true and R is true, P is true.
If Q is true and R is true, P is false.
If Q is true and R is false, P is true.
If Q is true and R is false, P is false.
If Q is false and R is true, P is true.
If Q is false and R is true, P is false.
If Q is false and R is false, P is true.
If Q is false and R is false, P is false.
If P is true and R is true, Q is true.
If P is true and R is true, Q is false.
If P is false and R is true, Q is true.
If P is false and R is true, Q is false.
If P is false and R is false, Q is true.
If P is false and R is false, Q is false.
P may be true and at the same time Q may be false.
It is not possible that P is true and at the same time Q is false.
P may be true and at the same time R may be false.
It is not possible that P is true and at the same time R is false.
P may be false and at the same time Q may be true.
It is not possible that P is false and at the same time Q is true.
P may be false and at the same time R may be true.
It is not possible that P is false and at the same time R is true.

4. Q is true if and only if A is true and B is false.

If A is true and B is true, Q is true.
If A is true and B is true, Q is false.
If A is true and B is false, Q is true.
If A is true and B is false, Q is false.
If A is false and B is true, Q is true.
If A is false and B is true, Q is false.
If A is false and B is false, Q is true.
If A is false and B is false, Q is false.
If Q is true and B is false, A is true.
If Q is true and B is false, A is false.
If Q is false and B is true, A is true.
If Q is false and B is true, A is false.
If Q is false and B is false, A is true.
If Q is false and B is false, A is false.
Q may be true and at the same time A may be false.
It is not possible that Q is true and at the same time A is false.
Q may be true and at the same time B may be false.
It is not possible that Q is true and at the same time B is false.
Q may be false and at the same time A may be true.
It is not possible that Q is false and at the same time A is true.
Q may be false and at the same time B may be true.
It is not possible that Q is false and at the same time B is true.

5. R is true if and only if B is true or A is false.

If A is true and B is true, R is true.
If A is true and B is true, R is false.
If A is true and B is false, R is true.
If A is true and B is false, R is false.
If A is false and B is true, R is true.
If A is false and B is true, R is false.
If A is false and B is false, R is true.
If A is false and B is false, R is false.
If R is true and B is true, A is true.
If R is true and B is true, A is false.
If R is true and B is false, A is true.
If R is true and B is false, A is false.
If R is false and B is false, A is true.
If R is false and B is false, A is false.
R may be true and at the same time A may be false.
It is not possible that R is true and at the same time A is false.
R may be true and at the same time B may be false.
It is not possible that R is true and at the same time B is false.
R may be false and at the same time A may be true.
It is not possible that R is false and at the same time A is true.
R may be false and at the same time B may be true.
It is not possible that R is false and at the same time B is true.