ds-t2b

Be very careful of the quantification used in the

Info iconThis preview shows pages 2–4. Sign up to view the full content.

View Full Document Right Arrow Icon
[Be very careful of the quantification used in the induction step.] Basis Step: Induction Step: (c) Give a recursive definition of the set S of positive integers that are multiples of 4. Basis Step: Induction Step: 4. (10 pts.) Let {a n } be defined by the formula a n =3 n+2f o r n = 1,2,3,. ... Define the sequence {b n } recursively by b 1 = 5 and b n+1 =b n + 3 for n = 1,2,3,. ... Give a proof by induction that a n n for n = 1,2,3,. ...
Background image of page 2

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
TEST-2B/MAD2104 Page 3 of 4 5. (15 pts.) Label each of the following assertions with "true" or "false". Be sure to write out the entire word. (a) The set of all subsets of the natural numbers is not countable. (b) The number of functions from a set with 8 elements to a set with 15 elements is C(15,8). (c) The coeffient of x 3 y 5 in the expansion of (x + y) 8 is the number of 3-permutations of an 8 element set. (d) There is a one-to-one correspondence between the real numbers in the interval (-200,200) and the real numbers in the interval (0,1). (e) The total number of ways to assign truth values to five true-false problems by using the letters T and F is given by the sum below. 5 C(5,k) k=1 6. (10 pts.) What is the minimum number of students required in your Discrete Mathematics class to be sure that at least 4 have birthdays occurring in the same month this year? Explain.
Background image of page 3
TEST-2B/MAD2104 Page 4 of 4 7. (10 pts.) The following proposition represents an invalid argument form: [q (p q)] p.
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page2 / 4

Be very careful of the quantification used in the induction...

This preview shows document pages 2 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online