# Recent questions tagged kenneth-rosen

1
Find the sets $A$ and $B$ if $A-B=\left \{ 1,5,7,8 \right \}, B-A=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$
2
Prove the second absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cap (A \cup B) = A$
3
Prove the first absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cup (A \cup B) = A$
4
Let $A$ and $B$ be sets. Prove the commutative laws from Table 1 by showing that $A \cup B = B \cup A.$ $A \cap B = B \cap A.$
5
Show that $A- \phi = A.$ $\phi-A=\phi$
6
Prove the complement laws in Table 1 by showing that $A \cup \sim A = U.$ $A \cap \sim A=\phi.$
7
Prove the idempotent laws in Table 1 by showing that $A \cup A = A.$ $A \cap A=A.$
8
Prove the domination laws in Table 1 by showing that $A \cup U = U.$ $A \cap \phi=\phi.$
9
Prove the identity laws in Table 1 by showing that $A \cup \phi = A.$ $A \cap U=A.$
10
Prove the complement law in Table 1 by showing That $\sim \sim A = A.$
11
Let $A= \left \{ a,b,c,d,e \right \}$ and $B= \left \{ a,b,c,d,e,f,g,h \right \}$. Find $A \cup B$ $A \cap B$ $A-B$ $B-A$
1 vote
12
Let $A = \left \{ 1,2,3,4,5 \right \}$ and $B= \left \{ 0,3,6 \right \}$ .Find $A \cup B$ $A \cap B$ $A-B$ $B-A$
13
Suppose that $A$ is the set of sophomores at your school and $B$ is the set of students in discrete mathematics at your school. Express each of these sets in terms of $A$ and $B$ . the set of sophomores taking discrete mathematics in your ... are sophomores or are taking discrete mathematics the set of students at your school who either are not sophomores or are not taking discrete mathematics
14
Let $A$ be the set of students who live within one mile of school and let $B$ be the set of students who walk to classes. Describe the students in each of these sets. $A \cap B$ $A \cup B$ $A -B$ $B-A$
15
The defining property of an ordered pair is that two ordered pairs are equal if and only if their first elements are equal and their second elements are equal. Surprisingly, instead of taking the ordered pair as a primitive concept, we can construct ordered pairs using basic notions from set theory. Show that if ... $a = c$ and $b=d.$]
16
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^3>=1$ $Q(x) : x^2=2$ $R(x) : x<x^2$
17
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^2<3$ $Q(x) : x^2 >x$ $R(x): 2x+1 = 0$
18
Translate each of these quantifications into English and determine is truth value. $\exists x$ $\epsilon$ $R(x^3 = -1)$ $\exists x$ $\epsilon$ $Z (x+1>x)$ $\forall x$ $\epsilon$ $(x-1)$ $\epsilon$ Z $\forall x$ $\epsilon$ $Z (x^2$ $\epsilon$ $Z)$
19
Translate each of these quantifications into English and determine is truth value. $\forall x$ $\epsilon$ $(x^2 \neq -1)$ $\exists x$ $\epsilon$ $Z(x^2 =2)$ $\forall x$ $\epsilon$ $(x^2>0)$ $\forall x$ $\epsilon$ $R(x^2=x)$
20
Explain why $(A \times B) \times (C \times D)$ and $A \times (B \times C) \times D$ are not the same.
21
Explain why $A \times B \times C$ and $(A \times B) \times C$ are not the same.
22
Show that $A \times B \neq B \times A$, when $A$ and $B$ are nonempty. unless $A = B.$
23
How many different elements does $A^n$ have when $A$ has $m$ elements and $n$ is a positive integer?
24
How many different elements does $A \times B \times C$ have it $A$ has $m$ elemetns, $B$ has $n$ elements, and $C$ has $p$ elements?
25
How many different elements does $A \times B$ have if $A$ has $m$ elements and $B$ has $n$ elements?
26
Find $A^3$ if $A=\left \{ a \right \}$ $A= \left \{ 0,a \right \}$
1 vote
27
Find $A^2$ if $A = \left \{ 0,1,3 \right \}$ $A = \left \{ 1,2,a,b \right \}$
Let $A = \left \{ a,b,c \right \}$, $B = \left \{ x,y \right \},$ and $C= \left \{ 0,1 \right \}$. Find $A \times B \times C$ $C \times B \times A$ $C \times A \times B$ $B \times B \times B$
Let $A$ be a set. Show that $\phi \times A = A \times \phi = \phi$
Suppose that $A \times B = \phi$, where $A$ and $B$ are sets. What can you conclude?