f(u) = the language that u speaks. Then the function f is well defined. O True False

let A be a set with n elements and B a set with m elements. How many different functions are there from A to B? Explain. If we assume n ≤ m, ho wmany one-to-one functions from A to B are there? Explain. If we assume n > m, how many one-to-one functions from A to B are there? Explain

Which among the following statements is true? * Let A be a non-empty set and f,g,h:A –A be any bijective functions. Then the inverse of hogof exists. Every function has an inverse. Let f be a function. Then the image O of a non-empty subset of the domain of f can be empty. All of these None of these

Suppose that ? = {2, 4, 6}, ? = {2, 6}, ? = {4, 6} ??? ? = {4, 6, 8}. Determine which of these sets are subsets of the other sets. b. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one.i. f(a) = b, f(b) = a, f(c) = c, f(d) = d ii. f(a) = b, f(b) = b, f(c) = d, f(d) = c iii. f(a) = d, f(b) = b, f(c) = c, f(d) = d c. Write in symbols: ′??? ??? ?, ? < 5 ?? ? ≥ 5′ d. Express the following propositions in symbolic form, and identify the principal connective:i. Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics. ii. It is not the case that if it is sunny then I will carry an umbrella.

⁸What is the correct aanswer

(Set theory)

Give a proof of the following statement. Suppose A, B and C are sets, f is an injective function from A to B, and g is an injective function from B to C. Then g • f is injective.

Give an example of a function from the set of all integers to the set of all negative even integers that is onto, but not one-to-one. For the case of not one-to-one, give a counterexample. For the case of onto state briefly why you think the function is onto. You do not need to create a formal 2-column statement/justification proof that the function is onto. Piecewise functions are acceptable if properly defined.

They're all a YES OR NO question :)