i.) Describe a proper subset A c N such that a surjective function f exists from
ID: 2984888 • Letter: I
Question
i.) Describe a proper subset A c N such that a surjective function f exists from A to N.
ii.) Consider a set of 17 distinct letters of the English alphabet. Calculate the number of 5 letter words whose letters are in alphabetic order.
iii.) A car manufacturer builds four models, allowing twelve colors, three engine sizes and either manual or automatic transmission. How many different varieties are there?
iv.) Consider two sets S1 and S2. How many relations are there from S1 to S2?
v.) Let A = {0,1} and B = {2,3}, what is the powerset of A and what is the caresian product of B and A?
vi.) Let A = {a1, a2, a3, a4, a5, a6} be 6 distinct numbers from 1 to 10. Let B be the powerset of A and let a function f be constructed which maps an element of B to the sum of all values in the element of B chosen. a.) What is the cardinality of the domain? b.) What is the maximum possible value of f? c.) what is the maximum possible cardinality of the codomain? d.) why would the size of the range most probably be less than that of the codomain?
Explanation / Answer
(i) A = {2k : k belongs to N} i.e A is the set of all even natural numbers.Observe f : A -> N f(2k) = k is a surjection.
(ii) 17C5 (need to choose 5 letters,for each such choice only one arrangement is in alphabetical order)
(iii) 4*12*3*2 = 288
(iv) 2^(|S1||S2|) (since any realation is a subset of cartesian product)
(v)Power set of A = {{},{0},{1},{0,1}}.
BxA = {(2,0)(2,1),(3,0),(3,1)}
(vi) (a)cardinality of domain = |B| = 2^6 = 64.
(b)maximum possible value of f is 10+9+8+7+6+5 = 45.
(c)maximum possible cardinality of codomain (asssuming we take codomain as fmin , fmin+1,...fmax) is 45 - 0 = 45
(d)Because there might be a natural number in between fmin and fmax such that there isn't any subset of B whose sum is equal to this number
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.