#include <vector>
using namespace std;

template <typename A>
class Relation
{
    vector<pair<A, A>> relations;
public:
    Relation() {}

    bool addPair(const A& a1, const A& a2) {
        auto p = make_pair<A, A>(a1, a2);
        if(count(relations.begin(), relations.end(), p) == 0)
            relations.push_back(p);
        return true;
    }

    bool hasPair(const A& a1, const A& a2) {
        auto p = make_pair<A, A>(a1, a2);
        return count(relations.begin(), relations.end(), p) != 0;
    }

    bool isReflexive() {
        for(auto i = 0; i < relations.size(); ++i) {
            if(!hasPair(relations[i].first, relations[i].first) ||
            !hasPair(relations[i].second, relations[i].second))
                return false;
        }
        return true;
    }

    bool isSymmetric() {
        for(auto i = 0; i < relations.size(); ++i) {
            if(!hasPair(relations[i].second, relations[i].first))
                return false;
        }
        return true;
    }

    bool isTransitive() {
        for(auto i = 0; i < relations.size() - 1; ++i) {
            for(auto j = i + 1; j < relations.size(); ++j) {
                if(!hasPair(relations[i].first, relations[j].second))
                    return false;
            }
        }
        return true;
    }
};