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Counting subsets of Finite sets: A student can choose a computer project from one of
three lists. The three lists contain 23, 15 and 19 possible projects, respectfully. No project is
on more than one list. How many possible projects are there to choose from?
Suppose that the universal set is U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}. Express each of these sets with bit
strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.
how to solve power set? {12,34,{45}, 56}
Problem 1. The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 20 salespeople given the information below.
Shift Average number of customers
Morning 95
Midday 305
Afternoon 435
Evening 115
Determine the apportionment using
a. Hamilton’s Method
b. Jefferson’s Method
c. Webster Method
d. Huntington-Hill Method
solve the recurrence relation Pn = Pn-1 + n with initial condition P1 = 2 using interation.
Use a predicates and quantifiers to express this statement. There is a man who has visited some park in every state of malaysia
Show that if x is a real number, then x − 1 < ⌊x⌋ ≤ x ≤
⌈x⌉ < x + 1.
Show that if x is a real number, then ⌈x⌉ − ⌊x⌋ = 1 if x is
not an integer and ⌈x⌉ − ⌊x⌋ = 0 if x is an integer.
Find the power set of each of these sets, where a and b are distinct elements.
a) {a} b) {a, b} c) {∅, {∅}}
Answer these questions for the poset ({3, 5, 9, 15, 24, 45}).
a) Find the maximal elements.
b) Find the minimal elements.
c) Is there a greatest element?
d) Is there a least element?
e) Find all upper bounds of { 5, 9}.
f ) Find the least upper bound of { 5, 9}, if it exists.
g) Find all lower bounds of {15, 24}.
h) Find the greatest lower bound of {15, 24}, if it exists.
#339914 on Dec 2023