. Let’s define on the set {1, 5, 7, 10, 12} the relation is such that if and only if the number is divisible by 4 without remainder. Construct the graph of this binary relation. Check whether is refle

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. Let’s define on the set {1, 5, 7, 10, 12} the relation is such that if and only if the number is divisible by 4 without remainder. Construct the graph of this binary relation. Check whether is reflexive, irreflexive, connected, symmetric, asymmetric, transitive, negatively transitive binary relation. Does this binary relation satisfy semitransitivity and strong intervality condition? Explain your answer (prove, if it is true, or provide a counterexample, if it not true).2. Prove that for any binary relation binary relations and are symmetric.3. Define the class (linear, weak, partial, interval order or semiorder) of these four binary relations from the picture below. If this binary relation belongs to several classes, write all of them.

4. A binary relation on a set of 6 elements contains 33 pairs. Can this binary relation be: a) symmetric, b) transitive? Prove or provide a counterexample.


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