E) given the following: let x = {1, 2, 3, 4) and a relation r on x as r= {(1,2), (2,3), (3,4)}. find the reflexive and transitive closure of r.

What’s the domain of this function? fast

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Solve this riddle: i am an odd number. i an less than 100. the some of my digit is 12. i am a multiple of 15. what number am i?