1. For any two relations E and F on the same set X , define a relation G := E ? F by xGz iff for some y, xEy and yFz. For each of the fol- lowing properties, if E and F both have the property, prove, or disprove by an example, that G also has the property: (a) reflexive, (b) symmetric, (c) transitive.
2. Refer to Problem 6 and answer the same question in regard to the following properties: (d) antisymmetric, (e) equivalence relation, (f) function.