f: {0, 1}4 → {0, 1}3 f(x) is obtained by removing the last two bits from x and adding a 1 to the end of the string. What is f(0000)? f(0000) = Ex: 111 Select all the strings in the range of f: 000 001 010 011 100 101 110 111

Let A = {-7, 0, 7} and B = {t, u, v, w}. Define a function F: A → B by the following arrow diagram: F A B и M. (a) What are the domain and co-domain of F? (Enter your answers in set-roster notation.) domain of F = co-domain of F = (b) F(-7) = F(0) = F(7) =

[D] Consider the function F: {1,5, 8} × {6, 10} → {0, 1, 2, 3, 4, 5} defined as follows: F: (a, b) → (4a + b)mod 6 (D.1) Fill in the ordered pairs in the diagram below to indicate the elements in the domain of F. Then draw in arrows to complete the diagram so that it correspondes to the function. ( • 0 • 1 • 2 • 3 • 4 • 5 (D.2) What is the range of F? (D.3) What is the co-domain of F? 3/5 (D.4) What is the preimage (inverse image) of 3? (D.5) What is the preimage (inverse image) of 0? (D.6) Is F one-to-one? If not provide a counterexample. (D.7) Is F onto? If not provide a counterexample.

f: (0, 1} (0, 1}3 f(x) is obtained by removing the second bit from x and placing the bit at the end of the string. For example, f(101) = 110. Select the correct description of the function f. O One-to-one and onto O Onto but not one-to-one O Neither one-to-one nor onto O One-to-one but not onto