MTH 154 Homework
Let A= {d, o, g}, B= {f, o, x} Find A x B and B x A.
(d,f),(d,o),(d,x),(o,f),(o,o),(o,x),(g,f),(g,o),(g,x) (f,d),(o,d),(x,d),(f,o),(o,o),(x,o),(f,g),(o,g),(x,g)
Use the given information to find n(A x B) and n(B x A) n(A)=84 and n(B) = 5 n(A x B) = ___ n(B x A)=
420 420
Suppose A and B are sets. Describe the conditions under which the following statement would be true. A= A-B
A∩B=∅
Suppose A and B are sets. Describe the conditions under which the following statement would be true. AuB = A
B C_ A
True or False (2,1) = (1,2)
False
Match the following term with the appropriate description A-F below. Assume A and B are sets. The difference in A and B
THe set of elements in A that are not in B
Describe the set (C - B)uA in words.
The set of all elements that are in C but not in B, or are in A.
Describe the following set in words. A u (B' n C')
The union of set A and the intersection of the complement of set B and the complement of set C.
Suppose A is a set. Describe the conditions under which the following statement is true. A = A- ∅
This statement is true for any set of A.
Let: U= {a, f, j, m, p, s, v} X= {a, j, p, v} Y= {a, f, j} Z= {f, j, m, p, s} Find the following set: (Z u X') ' n Y = {___}
a
Assuming that A and B represent any two sets, identify the statement as either always true or not always true. (AnB)C_A, is...
always true
The table, shown on the right, lists trees that are in two city parks. Let R be the set of trees in Riverside park and S be the set of trees in Sleepy Hollow PArk. Find the following set. R u S is {___}
b, d, m, o, p, s, w
Let D= {12,15,17}, E= {12,14,15,16} and F= {11,13,14,15,17} List the elements of D u E. D u E= {_____}
12,14,15,16,17
If n(A xB) = 700 and n(B)=20, find n(A) n(A)=___
35
If n(A x B) = 68 and n(A) = 17, find n(B). n(B)= ___
4
True or False {1, 7} = {7, 1}
True
Use the list of descriptions i-vi below. Assume A snd B are sets ... The difference of B and A can best be described by satement_____.
iv: The set of elements in B that are not in A.
For P = {9, 12, 13, 15}, Q= {2, 7, 11}, and R= {4, 7, 8, 11}, find P u (Q ∩ R) Hint- All of p then common elements of Q and R
{9,12, 13, 15 7, 11}
Let U= {1, 2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 5, 7}, and B= {2, 3, 4} Find the set A ∩ B. A ∩ B={____}
2
Given sets A, B, C, and U, find the elements in A - B'. A={3, 4, 6} B={0, 3, 4} C={5, 7} U={0, 1, 2, 3, 4, 5, 6, 7} A - B' = {___}
3, 4
Let U= {1, 2, 3, 4, 5, 6, 7}, A= {1, 2, 5, 7}, and B= {1, 4, 5}. Find the set A' ∩ B'. A' ∩ B'= {___} hint: all elements in U that are not present in A or B.
3, 6
Use the symbols A, B, C, u, n, and ' as needed to describe the shaded region. only circle B is shaded but inteloping areas of circle with all other circles is not shaded.
(A u C)' nB
Let U = {1, 2, 3, 4, 5}, A= {1, 2, 4}, and B = {1, 4, 5}, and C= {1, 2, 3}. (a)Find Au(BuC). (b)Find (AuB)uC. (c)State a conjecture. Use the results from (a) and (b) to answer this part.
(a)1,2,4,3,5 (b)1,2,3,4,5 (c)Au(BuC) = (AuB)uC
Use the results from parts (a) and (b) to answer part (c). Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A= {4, 5, 6, 9}, and B = {3, 6, 9}. (a) Find the set A n B (b)Find the set B n A (c) State a conjecture
(a)6, 9 (b)6, 9 (c) For any sets A and B, A n B = B n A.
Given sets A, B, C, and U, find the set B - A using the listing method. A={2, 3, 6} B={1, 2, 3, 7} C={5, 7} U={0, 1, 2, 3, 4, 5, 6, 7} B - A ={___} Hint- Lists the elements of B that are not in A
1, 7
Write a symbolic description of the following shaded area. Use the symbols A,K, n, u, -, and ' as necessary. all surrounding area of circles shaded only.
A' n K'
True or False (8,8) = (9-1,6+3)
False
Let U be the set of all tax returns, A be the set of all tax returns with standard deduction, B be the set of all tax returns showing business income, C be the set of all tax returns filed in 2007, and D be the set of all tax returns selected for audit. Describe the set C - Ain words.
The set of all tax returns filed in 2007 without deductions.
Let U be the set of all tax returns, A be the set of all tax returns with itemized deductions, B be the set of all tax returns showing business income, C be the set of all tax returns filed in 2009, and D be the set of all tax returns selected for audit. Describe the set (A u B) - D in words.
The set of all tax returns with itemized deductions or showing business income, but not selected for audit.
Let: U= all tax returns A= all tax returns with itemized deductions B= all tax returns showing business income C= all tax returns filed in 2011 D= all tax returns selected for audit. Describe the set (A n D) n B' in words.
The set of all tax returns with itemized deductions selected for audit but without business income.
Match the following term with the appropriate description A-F below. Assume A and B are sets. The intersection of A and B.
The set of elements common to both A and B
Write a description of the shaded region. Use the symbols Y, G, u, n, -, and '. just circle y is colored and not interlapping with circle g.
Y - G
Assuming that A and B represent any two sets, identify the statement as either always true or not always true. n(A u B)= n(A) + n(B) - n(A n B)
always true
Decide whether the given statement is always true or not always true. (AnB)C_A
always true
If A C_ B, the A n B = A is...
always true
Given sets X, Y, Z, and U, find the set Xn(X - Y) using the listing method. X= {d, e, c, b} Y= {d, g, b} Z= {g, e, f, c, a} U= {a, b, c, d, e, f, g} Xn(X - Y) = {___} hint, last 2 elements of X
c, b
Let U= {k, l, m, n, o, p, q} and A= {l, m, o, p}. Use the listing method to write the set A'. A'= {___}
k, n, q
Decide which elements should be put in region 4 given the information below. U= {b, c, f, g, m, o, p, t, v, w, x, y} A= {b, c, f, g, t, v} B= {g, m, o, p, t, v} List all of the elements that should be placed in region 4.
m, o, p
Explain why, if A and B are sets, it is not necessarily true that n(A - B) = n(A) - n(B). Give counterexample.
n(A-B) is equal to n(A) - n(B) only if every element in set B is contained within set A. So for example, if A= {2, 3, 4} and B= {3, 5} then n(A - B) not eqaul n(A) - n(B) because 2 notequal 1
Assuming that A and B represent any two sets, identify the statement as either always true or not always true. A C_(A n B) is...
not always true
Assuming that A and B represent any two sets, identify the statement as either always true or not always true. n(AuB)= n(A) + n(B) is...
not always true
Draw two appropriate Euler diagrams to decide whether the given statement is always true or not always true. If A C_ B, then A u B = A
not always true
Let: U= all tax returns A= all tax returns with itemized deductions B= all tax returns showing business income C= all tax returns filed in 2010 D= all tax returns selected for audit. Describe D u A' in words.
the set of all tax returns selected for audit or without itemized deductions
Match the following term with the appropriate description A-F below. Assume A and B are sets. The difference of B and A
the set of elements in B that are not in A
Match the following term with the appropriate description A-F below. Assume A and B are sets. The component of A
the set of elements in the universal set that are not in A
Match the following term with the appropriate description A-F below. Assume A and B are sets. the Cartesian product of A and B.
the set of ordered pairs such that each first element is from A and each second element is from B, with every element of A paired with every element of B.
The table lists some trees that are in two city parks. Let R be the set of trees in Riverside PArk, and S be the set of trees in SLeepy Hollow Park. Find the smallest universal set U that contains all listed trees of both options. ...
{sycamore, birch, dogwood, willow, oak, hickory, maple}