1. Use induction to prove: 2+4+6+···+2n=n(n+1) 2. Let S = {1, 2, ..., 8, 9}. Det
ID: 3774561 • Letter: 1
Question
1. Use induction to prove:
2+4+6+···+2n=n(n+1)
2. Let S = {1, 2, ..., 8, 9}. Determine whether or not each of the following is a partition of S :
(a) [{1,3,6},{2,8},{5,7,9}] (c) [{2,4,5,8},{1,9},{3,6,7}]
(b) [{1,5,7},{2,4,8,9},{3,5,6}] (d) [{1,2,7},{3,5},{4,6,8,9},{3,5}]
3. Examine the following Relations:
a. x y
b. Set inclusion on a collection C of sets.
Are relations (a) and (b)reflexive, symmetrical, transitive?
4. Given A = {1,2,3,4} and B = {x,y,z}. Let R be the following relation from A to B:
R = {(1, y), (1, z), (3, y), (4, x), (4, z)}
(a) Determine the matrix of the relation.
(b) Draw the arrow diagram of R.
(c) Find the inverse relation R1 of R.
(d) Determine the domain and range of R.
5. A license plate has 5 places, each having an alphanumeric value; how many license plates are we allowed to make? (repeating allowed)
6. Use Euclidian Algorithm to figure:
gcd(60,26)
7. How many hands consisting of 4 cards out of a 52 card deck?
Explanation / Answer
2. (c) [{2,4,5,8},{1,9},{3,6,7}]
7. The number of combinations of 4 cards from 52 cards is, 52C4
= 52! / [(52-4)! 4!]
= 52! / 48! 4!
= 270725
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