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Kenneth Rosen Edition 7th Exercise 2.2 Question 36 (Page No. 137)
Show that $A \oplus B = (AB) \cup (BA).$
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Apr 6, 2019
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Set Theory & Algebra
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Kenneth Rosen Edition 7th Exercise 2.2 Question 35 (Page No. 137)
Show that $A\oplus B = (A \cup B) – (A \cap B).$
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Kenneth Rosen Edition 7th Exercise 2.2 Question 32 (Page No. 137)
Find the symmetric difference of $\left \{ 1,3,5 \right \}$ and $\left \{ 1,2,3 \right \}.$
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20
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4
Kenneth Rosen Edition 7th Exercise 2.2 Question 31 (Page No. 137)
Let $A$ and $B$ be sbusets of a universal set $U$. Show that $A \subseteq B$ if and only if $ \sim B \subseteq \sim A.$
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5
Kenneth Rosen Edition 7th Exercise 2.2 Question 30 (Page No. 137)
Can you conclude that $A = B$ if $A,B,$ and $C$ are sets such that $A \cup C = B \cup C?$ $A \cap C = B \cap C?$ $A \cup C = B\cup C$ and $A \cap C = B \cap C?$
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9
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6
Kenneth Rosen Edition 7th Exercise 2.2 Question 29 (Page No. 136)
What can you say about the sets $A$ and $B$ if we know that $A \cup B = A?$ $A \cap B = A?$ $A B = A?$ $A \cap B =B \cap A?$ $A –B = BA?$
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7
Kenneth Rosen Edition 7th Exercise 2.2 Question 28 (Page No. 136)
Draw the Venn diagrams for each of these combinations of the sets $A,B,C,$ and $D.$ $(A \cap B) \cup (C \cap D)$ $ \sim A \cup \sim B \cup \sim C \cup \sim D$ $A (B \cap C \cap D)$
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Set Theory & Algebra
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8
Kenneth Rosen Edition 7th Exercise 2.2 Question 27 (Page No. 136)
Draw the Venn diagrams for each of these combinations of the sets $A,B,$ and $C$. $A \cap (BC)$ $(A \cap B) \cup (A \cap C)$ $(A \cap \sim B) \cup (A \cap \sim C)$
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Set Theory & Algebra
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Pooja Khatri
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15
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9
Kenneth Rosen Edition 7th Exercise 2.2 Question 26 (Page No. 136)
Draw the Venn diagrams for each of these combination sof the sets $A,B,$ and $C$. $A \cap (B \cup C)$ $\sim A \cap \sim B \cap \sim C$ $(AB) \cup (AC) \cup (BC)$
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Set Theory & Algebra
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Pooja Khatri
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7
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10
Kenneth Rosen Edition 7th Exercise 2.2 Question 25 (Page No. 136)
Let $A = \left \{ 0,2,4,6,8,10 \right \}, B=\left \{ 0,1,2,3,4,5,6 \right \},$ and $C =\left \{ 4,5,6,7,8,9,10 \right \}.$ Find $A \cap B \cap C.$ $A \cup B \cup C.$ $(A \cup B) \cap C.$ $(A \cap B) \cup C.$
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11
Kenneth Rosen Edition 7th Exercise 2.2 Question 24 (Page No. 136)
Let $A, B$ and $C$ be sets. Show that $(AB)C = (AC)(BC).$
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12
Kenneth Rosen Edition 7th Exercise 2.2 Question 23 (Page No. 136)
Prove the first distributive law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup(B \cap C) = (A \cup B) \cap (A \cup C).$
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Set Theory & Algebra
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8
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13
Kenneth Rosen Edition 7th Exercise 2.2 Question 22 (Page No. 136)
Prove the second associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cap C) = (A \cap B) \cap C.$
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Apr 6, 2019
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Set Theory & Algebra
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9
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14
Kenneth Rosen Edition 7th Exercise 2.2 Question 21 (Page No. 136)
Prove the first associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cup C)= (A \cup B) \cup C.$
asked
Apr 6, 2019
in
Set Theory & Algebra
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Pooja Khatri
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57
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0
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15
Kenneth Rosen Edition 7th Exercise 2.2 Question 20 (Page No. 136)
Show that if $A$ and $B$ are sets with $A \subseteq B,$ then $A \cup B = B$ $A \cap B = A$
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in
Set Theory & Algebra
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Pooja Khatri
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16
Kenneth Rosen Edition 7th Exercise 2.2 Question 19 (Page No. 136)
Show that if $A$ and $B$ are sets, then $AB = A \cap \sim B.$ $(A \cap B) \cup (A \cap \sim B)= A.$
asked
Apr 6, 2019
in
Set Theory & Algebra
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17
Kenneth Rosen Edition 7th Exercise 2.2 Question 18 (Page No. 136)
Let $A,B,$ and $C$ be sets, Show that $(A \cup B) \subseteq (A \cup B \cup C),$ $(A \cap B \cap C) \subseteq (A \cap B.)$ $(AB)C \subseteq AC.$ $(AC) \cap (CB) = \phi.$ $(BA) \cup (CA) = (B \cup C) A.$
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18
Kenneth Rosen Edition 7th 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$
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Apr 6, 2019
in
Set Theory & Algebra
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7
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19
Kenneth Rosen Edition 7th Exercise 2.2 Question 16 (Page No. 136)
Let $A$ and $B$ be sets. Show that $(A \cap B) \subseteq A.$ $A \subseteq (A \subseteq B.)$ $AB \subseteq A.$ $A \cap(BA) = \phi$
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20
Kenneth Rosen Edition 7th 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.
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6
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0
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1
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21
Kenneth Rosen Edition 7th Exercise 2.2 Question 14 (Page No. 136)
Find the sets $A$ and $B$ if $AB=\left \{ 1,5,7,8 \right \}, BA=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$
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Set Theory & Algebra
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10.9k
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21
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kennethrosen
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0
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22
Kenneth Rosen Edition 7th 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 $A \cap (A \cup B) = A$
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23
Kenneth Rosen Edition 7th 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 $A \cup (A \cup B) = A$
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24
Kenneth Rosen Edition 7th Exercise 2.2 Question 11 (Page No. 136)
Let $A$ and $B$ be sets. Prove the commutative laws from Table 1 by showing that $A \cup B = B \cup A.$ $A \cap B = B \cap A.$
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25
Kenneth Rosen Edition 7th Exercise 2.2 Question 10 (Page No. 136)
Show that $A \phi = A.$ $\phiA=\phi$
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26
Kenneth Rosen Edition 7th Exercise 2.2 Question 9 (Page No. 136)
Prove the complement laws in Table 1 by showing that $A \cup \sim A = U.$ $A \cap \sim A=\phi.$
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27
Kenneth Rosen Edition 7th Exercise 2.2 Question 8 (Page No. 136)
Prove the idempotent laws in Table 1 by showing that $A \cup A = A.$ $A \cap A=A.$
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28
Kenneth Rosen Edition 7th Exercise 2.2 Question 7 (Page No. 136)
Prove the domination laws in Table 1 by showing that $A \cup U = U.$ $A \cap \phi=\phi.$
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29
Kenneth Rosen Edition 7th Exercise 2.2 Question 6 (Page No. 136)
Prove the identity laws in Table 1 by showing that $A \cup \phi = A.$ $A \cap U=A.$
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Pooja Khatri
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30
Kenneth Rosen Edition 7th Exercise 2.2 Question 5 (Page No. 136)
Prove the complement law in Table 1 by showing That $\sim \sim A = A.$
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in
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by
Pooja Khatri
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(
10.9k
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12
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