Interactive exercises on Sets, Relations, etc.

Symmetric Difference of Sets

In the following dynamical Venn diagram, drag the points P, Q and R in such positions that

1) P belongs to the set A \B

2) Q belongs to the set B \A

3) R belongs to the complement of (A \B) È(B \A)

Element and sets

Move the element P so that the statement

(S)       (A Ç B) \ C = {P}

becomes true.

Truth values of a statement

Choose the right truth values of P Ú (Q Ù R), depending on the truth values of P, Q and R.

1. You may test each item by using the dynamical "electric circuit" figure.
2. After having clicked all choices in the table rows you can check whether all your choices are correct (Evaluate-button).

Truth values P Ú (Q Ù R)
P Q R 1 = true 0 = false
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0

Equivalence classes

The following relation E is an equivalence relation in the set X:
E = { (a, a), (a, c), (a, e), (b, b), (b, f), (c, a), (c, c),(c, e), (d, d), (e, a), (e, c), (e, e), (f, b), (f, f) }
Drag the elements to the equivalence classes induced by E.

Equivalence classes of equivalence closure

Equivalence closure of a relation R is the smallest equivalence relation which contains the relation R.
Move the elements to the equivalence classes that are induced by the equivalence closure of the relation in the left figure.