Let
U={1,2, 3, ...,3200}.
Let S be the subset of the numbers in U that are...
Let
U={1,2, 3, ...,3200}.
Let S be the subset of the numbers in U that are multiples of
4, and let T be the subset of U that are multiples of 9. Since
3200 divided by 4 equals it follows that
n(S)=n({4*1,4*2,...,4*800})=800
(a) Find n(T) using a method similar to the one that showed
that n(S)=800
(b) Find n(S∩T).
(c) Label the number of elements in each region of a two-loop
Venn diagram with the universe U and subsets S...
1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be
the power set of D,...
1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be
the power set of D, i.e. the set of all subsets of D.
a) How many elements are there in P(D)? Prove
it!
b) Which number is greater: the number of different
subsets of D which contain the digit 7 or the number of different
subsets of D which do not contain the digit 7? Explain why!
c) Which number is greater: the number of different...
Let A be the last two digits, let B be the last digit, and let C...
Let A be the last two digits, let B be the last digit, and let C
be the sum of the last three digits of your 8-digit
student ID. Example: for 20245347, A = 47, B = 7, and C = 14.
Consider two carts on a track. Cart A with mass mA =
(0.300 + (A/100)) kg has a speed of (2.50 + B) m/s before colliding
with and sticking to cart B. Cart has a mass mB =...
Let A be the last two digits, let B be the last digit,
and let C...
Let A be the last two digits, let B be the last digit,
and let C be the sum of the last three digits of your
8-digit student ID. Example: for 20245347, A = 47, B = 7, and C =
14.
A container with (15.0 + A) g of water at (8.0 + C)
oC is placed in a freezer. How much heat must be removed
from the water to turn it to ice at –(5.0 + B) oC?...
question 1: Let A be the last digit, let B be the second to last
digit,...
question 1: Let A be the last digit, let B be the second to last
digit, and let C be the sum of the last three digits of your
8-digit student ID. Example: for 20245347, A = 7, B = 4, and C =
14.
Starting from rest, a student pulls a (25.0+A) kg box a distance
of (4.50 + B) m across the floor using a (134 + C) N force applied
at 35.0 degrees above horizontal. The coefficient...
1. a) Let f : C → D be a function. Prove that if C1
and...
1. a) Let f : C → D be a function. Prove that if C1
and C2 be two subsets of C, then
f(C1ꓴC2) = f(C1) ꓴ
f(C2).
b) Let f : C → D be a function. Let C1 and C2
be subsets of C. Give an example of
sets C, C1, C2 and D for which f(C ꓵ D) ≠
f(C1) ꓵ f(C2).
1) Let A = {1, 2, · · · , 10} and B = {1,2,3, a,...
1) Let A = {1, 2, · · · , 10} and B = {1,2,3, a, b, c, d}
then |A ∩B|=
2) How many 8 digit telephone numbers can be made from {0, 1, 2,
3, 4, 5, 6, 7, 8, 9} such that the first digit is not 0?
(Repetition of a digit is allowed.)
3) Let A = {1, 2, · · · , 10} and B = {1,2,3, a, b, c, d}
then |A − B|=
4) Let A =...
4. Let a = 24, b = 105 and c = 594.
(a) Find the prime...
4. Let a = 24, b = 105 and c = 594.
(a) Find the prime factorization of a, b and c.
(b) Use (a) to calculate d(a), d(b) and d(c), where, for any
integer n, d(n) is the number of positive divisors of n;
(c) Use (a) to calculate σ(a), σ(b) and σ(c), where, for any
integer n, σ(n) is the sum of positive divisors of n;
(d) Give the list of positive divisors of a, b and c.
Let A,BA,B, and CC be sets such that |A|=11|A|=11, |B|=7|B|=7
and |C|=10|C|=10. For each element (x,y)∈A×A(x,y)∈A×A,...
Let A,BA,B, and CC be sets such that |A|=11|A|=11, |B|=7|B|=7
and |C|=10|C|=10. For each element (x,y)∈A×A(x,y)∈A×A, we associate
with it a one-to-one function f(x,y):B→Cf(x,y):B→C. Prove that
there will be two distinct elements of A×AA×A whose associated
functions have the same range.