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Class 10 Math Sets and Fractions 3. If U=N ; then verify De-Morgans laws by using A=\phi and B=P .


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3. If U=N ; then verify De-Morgans laws by using A=\phi and B=P .

6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(i) R_{1}=\{(11)(22)(33)(44)\}
6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(i)   R_{1}=\{(11)(22)(33)(44)\}

6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(i) R_{1}=\{(11)(22)(33)(44)\}

Example 1: Suppose A=\{2345\} and B=\{2468\} .Form a relation R: A \rightarrow B=\{x R y such that y=2 x for x \in A y \in B\}
Example 1: Suppose  A=\{2345\}  and  B=\{2468\} .Form a relation  R: A \rightarrow B=\{x R  y such that  y=2 x  for  x \in A y \in B\}

Example 1: Suppose A=\{2345\} and B=\{2468\} .Form a relation R: A \rightarrow B=\{x R y such that y=2 x for x \in A y \in B\}

3. Find a and -b if(ii) (2 \mathrm{a}+53)=(7 \mathrm{~b}-4)
3. Find  a  and  -b  if(ii)  (2 \mathrm{a}+53)=(7 \mathrm{~b}-4)

3. Find a and -b if(ii) (2 \mathrm{a}+53)=(7 \mathrm{~b}-4)

3. Find a and -b if(i) (a-4 b-2)=(21)
3. Find  a  and  -b  if(i)  (a-4 b-2)=(21)

3. Find a and -b if(i) (a-4 b-2)=(21)

3. Find a and b if(iii) (3-2 a b-1)=(a-72 b+5)
3. Find  a  and  b  if(iii)  (3-2 a b-1)=(a-72 b+5)

3. Find a and b if(iii) (3-2 a b-1)=(a-72 b+5)

2. If U=\{1234 \cdots 10\} A=\{13579\} ; B=\{14710\} ; C=\{15810\} then verify the following:(ii) (A \cap B) \cap C=A \cap(B \cap C)
2. If   U=\{1234 \cdots 10\}   A=\{13579\} ; B=\{14710\} ; C=\{15810\} then verify the following:(ii)  (A \cap B) \cap C=A \cap(B \cap C)

2. If U=\{1234 \cdots 10\} A=\{13579\} ; B=\{14710\} ; C=\{15810\} then verify the following:(ii) (A \cap B) \cap C=A \cap(B \cap C)

(xvii) The range of R=\{(13)(22) ;(31)(44)\} is(a) \{124\} (b) \{324\} (c) \{1234\} (d) \{134\}
(xvii) The range of  R=\{(13)(22) ;(31)(44)\}  is(a)  \{124\} (b)  \{324\} (c)  \{1234\} (d)  \{134\}

(xvii) The range of R=\{(13)(22) ;(31)(44)\} is(a) \{124\} (b) \{324\} (c) \{1234\} (d) \{134\}

4. If U=\{x \mid x \in N \wedge 3<x \leq 25\} X=\{x \mid x is prime \wedge 8<x<25\} and Y=\{x \mid x \in W \wedge 4 \leq x \leq 17\} .Find the value of:(i) (X \cup Y)^{\prime}
4. If  U=\{x \mid x \in N \wedge 3<x \leq 25\} X=\{x \mid x  is prime  \wedge 8<x<25\}  and  Y=\{x \mid x \in W \wedge 4 \leq x \leq 17\} .Find the value of:(i)  (X \cup Y)^{\prime}

4. If U=\{x \mid x \in N \wedge 3<x \leq 25\} X=\{x \mid x is prime \wedge 8<x<25\} and Y=\{x \mid x \in W \wedge 4 \leq x \leq 17\} .Find the value of:(i) (X \cup Y)^{\prime}

3. If U=N ; then verify De-Morgans laws by using A=\phi and B=P .
3. If  U=N ; then verify De-Morgans laws by using  A=\phi  and  B=P .
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3. If U=N ; then verify De-Morgans laws by using A=\phi and B=P .

1. If X=\{1479\} and Y=\{2459\} Then find:(iv) Y \cap X
1. If  X=\{1479\}  and  Y=\{2459\} Then find:(iv)  Y \cap X

1. If X=\{1479\} and Y=\{2459\} Then find:(iv) Y \cap X

3. If X=\phi Y=Z^{+} T=O^{+} then find:(i) X \cup Y
3. If  X=\phi Y=Z^{+} T=O^{+}  then find:(i)  X \cup Y

3. If X=\phi Y=Z^{+} T=O^{+} then find:(i) X \cup Y

2. If U=\{1234 \cdots 10\} A=\{13579\} ; B=\{14710\} ; C=\{15810\} then verify the following:(i) (A \cup B) \cup C=A \cup(B \cup C)
2. If   U=\{1234 \cdots 10\}   A=\{13579\} ; B=\{14710\} ; C=\{15810\} then verify the following:(i)  (A \cup B) \cup C=A \cup(B \cup C)

2. If U=\{1234 \cdots 10\} A=\{13579\} ; B=\{14710\} ; C=\{15810\} then verify the following:(i) (A \cup B) \cup C=A \cup(B \cup C)

(xiii) A \cup(B \cap C) is equal to(a) (A \cup B) \cap(A \cup C) (c) (A \cap B) \cup(A \cap C) (b) A \cap(B \cap C) (d) A \cup(B \cup C)
(xiii)  A \cup(B \cap C)  is equal to(a)  (A \cup B) \cap(A \cup C) (c)  (A \cap B) \cup(A \cap C) (b)  A \cap(B \cap C) (d)  A \cup(B \cup C)

(xiii) A \cup(B \cap C) is equal to(a) (A \cup B) \cap(A \cup C) (c) (A \cap B) \cup(A \cap C) (b) A \cap(B \cap C) (d) A \cup(B \cup C)

(x) If A \subseteq B then A \cap B is equal to(a) A (b) B (c) \phi (d) none of these
(x) If  A \subseteq B  then  A \cap B  is equal to(a)  A (b)  B (c)  \phi (d) none of these

(x) If A \subseteq B then A \cap B is equal to(a) A (b) B (c) \phi (d) none of these

\[\text { 1. If } \begin{aligned}U &=\{1234 \cdots 10\} \\A &=\{13579\} \\B &=\{14710\}\end{aligned}\]then verify the following questions.(iv) (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}
\[\text { 1. If }  \begin{aligned}U &=\{1234 \cdots 10\} \\A &=\{13579\} \\B &=\{14710\}\end{aligned}\]then verify the following questions.(iv)  (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}

\[\text { 1. If } \begin{aligned}U &=\{1234 \cdots 10\} \\A &=\{13579\} \\B &=\{14710\}\end{aligned}\]then verify the following questions.(iv) (A \cap B)^{\prime}=A^{\prime} \cup B^{\prime}

(xi) If A \subseteq B then A-B is equal to(a) A (b) B (c) \phi (d) B-A
(xi) If  A \subseteq B  then  A-B  is equal to(a)  A (b)  B (c)  \phi (d)  B-A

(xi) If A \subseteq B then A-B is equal to(a) A (b) B (c) \phi (d) B-A

6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(iv) R_{4}=\{(11)(23)(34)(43)(54)\}
6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(iv)   R_{4}=\{(11)(23)(34)(43)(54)\}

6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(iv) R_{4}=\{(11)(23)(34)(43)(54)\}

4. If U=\{1234 \cdots 10\} A=\{13579\} and B=\{23458\} then prove the following questions by Venn diagram:(v) (A-B)^{\prime}=A^{\prime} \cup B
4. If  U=\{1234 \cdots 10\} A=\{13579\}  and  B=\{23458\}  then prove the following questions by Venn diagram:(v)  (A-B)^{\prime}=A^{\prime} \cup B

4. If U=\{1234 \cdots 10\} A=\{13579\} and B=\{23458\} then prove the following questions by Venn diagram:(v) (A-B)^{\prime}=A^{\prime} \cup B

2. Write short answers of the following questions.(viii) Define an onto function.
2. Write short answers of the following questions.(viii) Define an onto function.
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2. Write short answers of the following questions.(viii) Define an onto function.

\[\text { 1. If } \begin{aligned}U &=\{1234 \cdots 10\} \\A &=\{13579\} \\B &=\{14710\}\end{aligned}\]then verify the following questions.(v) (A-B)^{\prime}=A^{\prime} \cup B
\[\text { 1. If } \begin{aligned}U &=\{1234 \cdots 10\} \\A &=\{13579\} \\B &=\{14710\}\end{aligned}\]then verify the following questions.(v)  (A-B)^{\prime}=A^{\prime} \cup B
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\[\text { 1. If } \begin{aligned}U &=\{1234 \cdots 10\} \\A &=\{13579\} \\B &=\{14710\}\end{aligned}\]then verify the following questions.(v) (A-B)^{\prime}=A^{\prime} \cup B

6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(iii) R_{3}=\{(b a)(c a)(d a)\}
6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(iii)   R_{3}=\{(b a)(c a)(d a)\}
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6. Indicate relations into function one-one function onto function and bijective function from the following. Also find their domain and the range. In each part from (i) to (vi) the co-domain set is taken equal to the range set.(iii) R_{3}=\{(b a)(c a)(d a)\}

2. If A=\{123456\} B=\{2468\} C=\{148\} . Prove the following identities:(i) A \cap B=B \cap A
2. If  A=\{123456\} B=\{2468\} C=\{148\} . Prove the following identities:(i)   A \cap B=B \cap A
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2. If A=\{123456\} B=\{2468\} C=\{148\} . Prove the following identities:(i) A \cap B=B \cap A

3. If L=\{a b c\} and M=\{d e f g\} then find two binary relations in each:(i) L \times L (ii) L \times M (iii) M \times M
3. If  L=\{a b c\}  and  M=\{d e f g\}  then find two binary relations in each:(i)   L \times L (ii)  L \times M (iii)  M \times M
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3. If L=\{a b c\} and M=\{d e f g\} then find two binary relations in each:(i) L \times L (ii) L \times M (iii) M \times M

Example 2: Suppose A=\{1234\} and B=\{1235\} Form a relation R: A \rightarrow B=\{x R y such that x+y=6 for x \in A y \in B\}
Example 2: Suppose  A=\{1234\}  and  B=\{1235\} Form a relation  R: A \rightarrow B=\{x R y  such that  x+y=6  for  x \in A y \in B\}
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Example 2: Suppose A=\{1234\} and B=\{1235\} Form a relation R: A \rightarrow B=\{x R y such that x+y=6 for x \in A y \in B\}

2. If Y=\{-212\} then make two binary relations for Y \times Y . Also find their domain and range.
2. If  Y=\{-212\}  then make two binary relations for  Y \times Y . Also find their domain and range.
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2. If Y=\{-212\} then make two binary relations for Y \times Y . Also find their domain and range.

3. If X=\phi Y=Z^{+} T=0^{+} then find:(iii) \simeq Y \cup T
3. If  X=\phi Y=Z^{+} T=0^{+}  then find:(iii)  \simeq Y \cup T
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3. If X=\phi Y=Z^{+} T=0^{+} then find:(iii) \simeq Y \cup T

3. If X=\phi Y=Z^{+} T=O^{+} then find:(ii) X \cup T
3. If  X=\phi Y=Z^{+} T=O^{+}  then find:(ii)   X \cup T
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3. If X=\phi Y=Z^{+} T=O^{+} then find:(ii) X \cup T

Example: If U=\{123 \ldots 10\} A=\{2357\} B=\{358\} then find (i) A \cup B
Example: If  U=\{123 \ldots 10\} A=\{2357\} B=\{358\}  then find (i)  A \cup B
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Example: If U=\{123 \ldots 10\} A=\{2357\} B=\{358\} then find (i) A \cup B

5. If X=\{246 \cdots 20\} and Y=\{4812 \cdots 24\} then find the following:(i) X-Y
5. If  X=\{246 \cdots 20\}  and  Y=\{4812 \cdots 24\}  then find the following:(i)  X-Y
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5. If X=\{246 \cdots 20\} and Y=\{4812 \cdots 24\} then find the following:(i) X-Y

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