(1) Make a PERT diagram for the following problem and determine the
project time and the critical path.
Table 1. default
task time preceeding tasks
A 5 none
B 9 A
C 10 A, F
D 7 B, C
E 2 none
F 4 E
G 11 E
H 9 F, G
I 6 D, H
(2) A make-up kit contains 3 moustaches, 3 eyebrows, 5 noses and 2 sets of
ears. What is the number of possible disguises using at least one item?
(3) A draw poker player can discard some but not all of his 5cards for new
ones. How many choices does a player have?
(4) Determine the complexity of the following polynomial evaluation algo-
rithm:
Input: nonnegative integer nand real numbers x, a0, a1, . . . , an;
output: P(x) = a0+a1x+a2x2+· · · +anxn.
Step 1. (initialization) Set S=a0and k=1;
Step 2. (add the next term)
while k≤n
•Replace Swith S+akxk;
•Replace kwith k+1.
endwhile
Step 3. Print S.
You may use the fact that the complexity for computing xmis 3m −2
and that
1+2+· · · +k=k(k+1)
2.
(5) Show that p→(q∨r)and (p→q)∨(p→r)are logically equivalent.
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