Recent questions in Discrete Mathematics / GATE Overflow for GATE CSE

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1641

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

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Pooja Khatri asked Apr 6, 2019

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1642

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

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Pooja Khatri asked Apr 6, 2019

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1643

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

253 views

Pooja Khatri asked Apr 6, 2019

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1644

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

193 views

Pooja Khatri asked Apr 6, 2019

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1645

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

169 views

Pooja Khatri asked Apr 6, 2019

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1646

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

137 views

Pooja Khatri asked Apr 6, 2019

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1647

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

125 views

Pooja Khatri asked Apr 6, 2019

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1648

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

134 views

Pooja Khatri asked Apr 6, 2019

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1649

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

181 views

Pooja Khatri asked Apr 6, 2019

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1650

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

198 views

Pooja Khatri asked Apr 6, 2019

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1651

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

185 views

Pooja Khatri asked Apr 6, 2019

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1652

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

190 views

Pooja Khatri asked Apr 6, 2019

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1 answer

1653

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

251 views

Pooja Khatri asked Apr 6, 2019

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1 answer

1654

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

284 views

Pooja Khatri asked Apr 5, 2019

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1655

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

359 views

Pooja Khatri asked Apr 5, 2019

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1656

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

233 views

Pooja Khatri asked Apr 5, 2019

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1657

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

452 views

Pooja Khatri asked Apr 5, 2019

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1658

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

260 views

Pooja Khatri asked Apr 5, 2019

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1659

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

197 views

Pooja Khatri asked Apr 5, 2019

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1660

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

207 views

Pooja Khatri asked Apr 5, 2019

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