Recent questions tagged kenneth-rosen / GATE Overflow for GATE CSE

Let $A,B,$ and $C$ be sets, Show that$(A \cup B) \subseteq (A \cup B \cup C),$$(A \cap B \cap C) \subseteq (A \cap B.)$$(A-B)-C \subseteq A-C.$$(A-C) \cap (C-B) = \phi.$$...

Pooja Khatri

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Pooja Khatri asked Apr 6, 2019

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635

Kenneth Rosen Edition 7 Exercise 2.2 Question 17 (Page No. 136)
Show that if $A,B,$ and $C$ are sets, then $ \sim (A \cap B \cap C) = \sim A \cup \sim B \cup \sim C$

Show that if $A,B,$ and $C$ are sets, then $ \sim (A \cap B \cap C) = \sim A \cup \sim B \cup \sim C$

Pooja Khatri

154 views

Pooja Khatri asked Apr 6, 2019

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636

Kenneth Rosen Edition 7 Exercise 2.2 Question 16 (Page No. 136)
Let $A$ and $B$ be sets. Show that $(A \cap B) \subseteq A.$ $A \subseteq (A \subseteq B.)$ $A-B \subseteq A.$ $A \cap(B-A) = \phi$

Let $A$ and $B$ be sets. Show that$(A \cap B) \subseteq A.$$A \subseteq (A \subseteq B.)$$A-B \subseteq A.$$A \cap(B-A) = \phi$

Pooja Khatri

158 views

Pooja Khatri asked Apr 6, 2019

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637

Kenneth Rosen Edition 7 Exercise 2.2 Question 15 (Page No. 136)
rove the second De Morgan law in Table 1 by showing that if $A$ and $B$ are sets, then $\sim (A \cup B) = (\sim A \cap \sim B)$ by showing each side is a subset of the other side. using a membership table.

rove the second De Morgan law in Table 1 by showing that if $A$ and $B$ are sets, then $\sim (A \cup B) = (\sim A \cap \sim B)$by showing each side is a subset of the oth...

Pooja Khatri

165 views

Pooja Khatri asked Apr 6, 2019

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1 answer

638

Kenneth Rosen Edition 7 Exercise 2.2 Question 14 (Page No. 136)
Find the sets $A$ and $B$ if $A-B=\left \{ 1,5,7,8 \right \}, B-A=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$

Find the sets $A$ and $B$ if $A-B=\left \{ 1,5,7,8 \right \}, B-A=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$

Pooja Khatri

248 views

Pooja Khatri asked Apr 6, 2019

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639

Kenneth Rosen Edition 7 Exercise 2.2 Question 13 (Page No. 136)
Prove the second absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cap (A \cup B) = A$

Prove the second absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cap (A \cup B) = A$

Pooja Khatri

188 views

Pooja Khatri asked Apr 6, 2019

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640

Kenneth Rosen Edition 7 Exercise 2.2 Question 12 (Page No. 136)
Prove the first absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cup (A \cup B) = A$

Prove the first absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cup (A \cup B) = A$

Pooja Khatri

164 views

Pooja Khatri asked Apr 6, 2019

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641

Kenneth Rosen Edition 7 Exercise 2.2 Question 11 (Page No. 136)
Let $A$ and $B$ be sets. Prove the commutative laws from Table 1 by showing that $A \cup B = B \cup A.$ $A \cap B = B \cap A.$

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.$

Pooja Khatri

134 views

Pooja Khatri asked Apr 6, 2019

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642

Kenneth Rosen Edition 7 Exercise 2.2 Question 10 (Page No. 136)
Show that $A- \phi = A.$ $\phi-A=\phi$

Show that$A- \phi = A.$$\phi-A=\phi$

Pooja Khatri

121 views

Pooja Khatri asked Apr 6, 2019

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643

Kenneth Rosen Edition 7 Exercise 2.2 Question 9 (Page No. 136)
Prove the complement laws in Table 1 by showing that $A \cup \sim A = U.$ $A \cap \sim A=\phi.$

Prove the complement laws in Table 1 by showing that$A \cup \sim A = U.$$A \cap \sim A=\phi.$

Pooja Khatri

132 views

Pooja Khatri asked Apr 6, 2019

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644

Kenneth Rosen Edition 7 Exercise 2.2 Question 8 (Page No. 136)
Prove the idempotent laws in Table 1 by showing that $A \cup A = A.$ $A \cap A=A.$

Prove the idempotent laws in Table 1 by showing that$A \cup A = A.$$A \cap A=A.$

Pooja Khatri

177 views

Pooja Khatri asked Apr 6, 2019

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0 answers

645

Kenneth Rosen Edition 7 Exercise 2.2 Question 7 (Page No. 136)
Prove the domination laws in Table 1 by showing that $A \cup U = U.$ $A \cap \phi=\phi.$

Prove the domination laws in Table 1 by showing that$A \cup U = U.$$A \cap \phi=\phi.$

Pooja Khatri

194 views

Pooja Khatri asked Apr 6, 2019

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0 answers

646

Kenneth Rosen Edition 7 Exercise 2.2 Question 6 (Page No. 136)
Prove the identity laws in Table 1 by showing that $A \cup \phi = A.$ $A \cap U=A.$

Prove the identity laws in Table 1 by showing that$A \cup \phi = A.$$A \cap U=A.$

Pooja Khatri

182 views

Pooja Khatri asked Apr 6, 2019

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0 answers

647

Kenneth Rosen Edition 7 Exercise 2.2 Question 5 (Page No. 136)
Prove the complement law in Table 1 by showing That $\sim \sim A = A.$

Prove the complement law in Table 1 by showing That $\sim \sim A = A.$

Pooja Khatri

186 views

Pooja Khatri asked Apr 6, 2019

0 votes

1 answer

648

Kenneth Rosen Edition 7 Exercise 2.2 Question 4 (Page No. 136)
Let $A= \left \{ a,b,c,d,e \right \}$ and $B= \left \{ a,b,c,d,e,f,g,h \right \}$. Find $A \cup B$ $A \cap B$ $A-B$ $B-A$

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$

Pooja Khatri

247 views

Pooja Khatri asked Apr 6, 2019

1 votes

1 answer

649

Kenneth Rosen Edition 7 Exercise 2.2 Question 3 (Page No. 136)
Let $A = \left \{ 1,2,3,4,5 \right \}$ and $B= \left \{ 0,3,6 \right \}$ .Find $A \cup B$ $A \cap B$ $A-B$ $B-A$

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$

Pooja Khatri

277 views

Pooja Khatri asked Apr 5, 2019

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650

Kenneth Rosen Edition 7 Exercise 2.2 Question 2 (Page No. 136)
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 ... are taking discrete mathematics the set of students at your school who either are not sophomores or are not taking discrete mathematics

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 $A$...

Pooja Khatri

342 views

Pooja Khatri asked Apr 5, 2019

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651

Kenneth Rosen Edition 7 Exercise 2.2 Question 1 (Page No. 136)
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. $A \cap B$ $A \cup B$ $A -B$ $B-A$

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 \...

Pooja Khatri

228 views

Pooja Khatri asked Apr 5, 2019

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652

Kenneth Rosen Edition 7 Exercise 2.1 Question 45 (Page No. 126)
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 ... $a = c$ and $b=d.$]

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. Surprising...

Pooja Khatri

449 views

Pooja Khatri asked Apr 5, 2019

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0 answers

653

Kenneth Rosen Edition 7 Exercise 2.1 Question 44 (Page No. 126)
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^3>=1$ $Q(x) : x^2=2$ $R(x) : x<x^2$

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$

Pooja Khatri

258 views

Pooja Khatri asked Apr 5, 2019

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654

Kenneth Rosen Edition 7 Exercise 2.1 Question 43 (Page No. 126)
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^2<3$ $Q(x) : x^2 >x$ $R(x): 2x+1 = 0$

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$

Pooja Khatri

193 views

Pooja Khatri asked Apr 5, 2019

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655

Kenneth Rosen Edition 7 Exercise 2.1 Question 42 (Page No. 126)
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 $ $\epsilon$ $Z)$

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$ $\epsi...

Pooja Khatri

205 views

Pooja Khatri asked Apr 5, 2019

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656

Kenneth Rosen Edition 7 Exercise 2.1 Question 41 (Page No. 126)
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) $ $\forall x$ $\epsilon$ $(x^2>0)$ $\forall x$ $\epsilon$ $R(x^2=x)$

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$ $\e...

Pooja Khatri

229 views

Pooja Khatri asked Apr 5, 2019

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657

Kenneth Rosen Edition 7 Exercise 2.1 Question 40 (Page No. 126)
Explain why $(A \times B) \times (C \times D)$ and $A \times (B \times C) \times D$ are not the same.

Explain why $(A \times B) \times (C \times D)$ and $A \times (B \times C) \times D$ are not the same.

Pooja Khatri

184 views

Pooja Khatri asked Apr 5, 2019

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658

Kenneth Rosen Edition 7 Exercise 2.1 Question 39 (Page No. 126)
Explain why $A \times B \times C$ and $(A \times B) \times C$ are not the same.

Explain why $A \times B \times C$ and $(A \times B) \times C$ are not the same.

Pooja Khatri

166 views

Pooja Khatri asked Apr 5, 2019

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659

Kenneth Rosen Edition 7 Exercise 2.1 Question 38 (Page No. 126)
Show that $A \times B \neq B \times A$, when $A$ and $B$ are nonempty. unless $A = B.$

Show that $A \times B \neq B \times A$, when $A$ and $B$ are nonempty. unless $A = B.$

Pooja Khatri

159 views

Pooja Khatri asked Apr 5, 2019

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660

Kenneth Rosen Edition 7 Exercise 2.1 Question 37 (Page No. 126)
How many different elements does $A^n$ have when $A$ has $m$ elements and $n$ is a positive integer?

How many different elements does $A^n$ have when $A$ has $m$ elements and $n$ is a positive integer?

Pooja Khatri

241 views

Pooja Khatri asked Apr 5, 2019

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