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Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

 If A = {10, 20,30, 40 },  B = {12,20,24,36,48}  and C = {14,20,24,28,42,56} then find ,

verify whether A\(B\C) = (A\B)∖C. Justify your Answer.








Answer:_______________




2)  

Given P = {3,6,8,9,-7},  Q = {3,-7,-2,-9,9} and R = {3,8,14,-7}.Find the  property of set intersection.






Answer:_______________




3)  

 Give A = {J,Y,V,M,K,4,7,8,7}   B = {4,13,7,-3,Y,V,M,K} very the  property of set intersection.







Answer:_______________




4)  

 Give A = {D,J,W,V,U}, B = {2,6,7,10,-15} very the  property of set union.






Answer:_______________




5)  

 If A = {15, 30,45, 60 },  B = {18,30,36,54,72}  and C = {21,30,36,42,63,84} then find ,

verify whether A\(B\C) = (A\B)∖C. Justify your Answer.








Answer:_______________




6)  

Given P = {2,5,8,9,-6},  Q = {2,-6,-2,-9,10} and R = {2,8,14,-6}.Find the  property of set intersection.






Answer:_______________




7)  

 Give A = {E,N,S,A,X,2,6,8,7}   B = {2,11,6,-5,N,S,A,X} very the  property of set intersection.







Answer:_______________




8)  

 Give A = {I,C,U,O,B}, B = {1,5,9,11,-16} very the  property of set union.






Answer:_______________




9)  

 If A = {20, 40,60, 80 },  B = {24,40,48,72,96}  and C = {28,40,48,56,84,112} then find ,

verify whether A\(B\C) = (A\B)∖C. Justify your Answer.








Answer:_______________




10)  

Given P = {4,6,7,9,-6},  Q = {4,-6,-3,-9,11} and R = {4,7,12,-6}.Find the  property of set intersection.






Answer:_______________




 

1)  

 If A = {10, 20,30, 40 },  B = {12,20,24,36,48}  and C = {14,20,24,28,42,56} then find ,

verify whether A\(B\C) = (A\B)∖C. Justify your Answer.





Answer: 3




SOLUTION 1 :

Solution:

 B∖C = {12,20,24,36,48} /{14,20,24,28,42,56} 

B∖C  =  {12,36,48}

A∖(B∖C)  = {10, 20,30, 40 } /  {12,36,48}

A(B /C)   = {10, 20,30, 40 } ......(1)

Now

(AB) =  {10, 20,30, 40 }/ {12,20,24,36,48}

       =  {10,30,40}

thus (AB) /C = {10,30,40} / {14,20,24,28,42,56} 

(AB) /B =  {10,30,40}   .........(2)

Hence from (1) and (2), We have A (BC)    ≠   (AB) /C

Justification :

Since the sets A,B,C are not mutually disjoint, the set difference is not associative.



2)  

Given P = {3,6,8,9,-7},  Q = {3,-7,-2,-9,9} and R = {3,8,14,-7}.Find the  property of set intersection.





Answer: 4


SOLUTION 1 :

 Given ; 

P = {3,6,8,9,-7}

Q = {3,-7,-2,-9,9}

R = {3,8,-7,14}

To verify : 

Associative property of intersection of sets.

(ie,) P∩(Q∩R)  = (P∩R)∩R

verification : 

      L.H.S =  P∩(Q∩R)

Now,          Q∩R = {3,-7,-2,-9,9}∩{3,8,-7,14}

                 Q∩R = {3,-7}

     ∴  P∩(Q∩R) = {3,6,8,9,-7}∩{3,-7}

          P∩(Q∩R) = {3,-7}

    R.H.S = (P∩R)∩R

Now,       P∩Q = {3,6,8,9,-7}∩{3,-7,-2,-9,9}

               P∩Q = {3,-7}

  ∴ (P∩Q)∩R = {3,-7}∩{3,8,-7,14}  

         (P∩Q)∩R =  {3,-7}

From (1) and (2), we have

P∩(Q∩R)  = (P∩R)∩R



3)  

 Give A = {S,J,X,B,P,4,7,8,7}   B = {4,13,7,-3,J,X,B,P} very the  property of set intersection.





Answer: 4



SOLUTION 1 :

Now     A∩B = {S,J,X,B,P,4,7,8,7} ∩ {4,13,7,-3,J,X,B,P}

                     = {J,X,B,4,7}      ........   (1)

Also      B∩A = {4,13,7,-3,J,X,B,P} ∩ {S,J,X,B,P,4,7,8,7}

          = {J,X,B,4,7}    .......  (2)

 

From (1) and (2) we have, A∩B = B∩A for the give sets A,B.

Hence the commutative property of set intersection verified.



4)  

 Give A = {D,Y,R,I,G}, B = {2,6,7,10,-15} very the  property of set union.





Answer: 2


SOLUTION 1 :

 Now     A∪B = {D,Y,R,I,G} ∪ {2,6,7,10,-15}

                     = {D,Y,R,I,G,2,6,7,10,-15}      ........   (1)

Also    B∪A = {2,6,7,10,-15} ∩ {D,Y,R,I,G}

          = {D,Y,R,I,G,2,6,7,10,-15}    .......  (2)

 

From (1) and (2) we have, A∪B = B∪A for the give sets A,B.

Hence the commutative property of set unios verified.



5)  

 If A = {15, 30,45, 60 },  B = {18,30,36,54,72}  and C = {21,30,36,42,63,84} then find ,

verify whether A\(B\C) = (A\B)∖C. Justify your Answer.





Answer: 4




SOLUTION 1 :

Solution:

 B∖C = {18,30,36,54,72} /{21,30,36,42,63,84} 

B∖C  =  {18,54,72}

A∖(B∖C)  = {15, 30,45, 60 } /  {18,54,72}

A(B /C)   = {15, 30,45, 60 } ......(1)

Now

(AB) =  {15, 30,45, 60 }/ {18,30,36,54,72}

       =  {15,45,60}

thus (AB) /C = {15,45,60} / {21,30,36,42,63,84} 

(AB) /B =  {15,45,60}   .........(2)

Hence from (1) and (2), We have A (BC)    ≠   (AB) /C

Justification :

Since the sets A,B,C are not mutually disjoint, the set difference is not associative.



6)  

Given P = {2,5,8,9,-6},  Q = {2,-6,-2,-9,10} and R = {2,8,14,-6}.Find the  property of set intersection.





Answer: 2


SOLUTION 1 :

 Given ; 

P = {2,5,8,9,-6}

Q = {2,-6,-2,-9,10}

R = {2,8,-6,14}

To verify : 

Associative property of intersection of sets.

(ie,) P∩(Q∩R)  = (P∩R)∩R

verification : 

      L.H.S =  P∩(Q∩R)

Now,          Q∩R = {2,-6,-2,-9,10}∩{2,8,-6,14}

                 Q∩R = {2,-6}

     ∴  P∩(Q∩R) = {2,5,8,9,-6}∩{2,-6}

          P∩(Q∩R) = {2,-6}

    R.H.S = (P∩R)∩R

Now,       P∩Q = {2,5,8,9,-6}∩{2,-6,-2,-9,10}

               P∩Q = {2,-6}

  ∴ (P∩Q)∩R = {2,-6}∩{2,8,-6,14}  

         (P∩Q)∩R =  {2,-6}

From (1) and (2), we have

P∩(Q∩R)  = (P∩R)∩R



7)  

 Give A = {Q,W,C,P,D,2,6,8,7}   B = {2,11,6,-5,W,C,P,D} very the  property of set intersection.





Answer: 1



SOLUTION 1 :

Now     A∩B = {Q,W,C,P,D,2,6,8,7} ∩ {2,11,6,-5,W,C,P,D}

                     = {W,C,P,2,6}      ........   (1)

Also      B∩A = {2,11,6,-5,W,C,P,D} ∩ {Q,W,C,P,D,2,6,8,7}

          = {W,C,P,2,6}    .......  (2)

 

From (1) and (2) we have, A∩B = B∩A for the give sets A,B.

Hence the commutative property of set intersection verified.



8)  

 Give A = {C,Y,K,J,S}, B = {1,5,9,11,-16} very the  property of set union.





Answer: 3


SOLUTION 1 :

 Now     A∪B = {C,Y,K,J,S} ∪ {1,5,9,11,-16}

                     = {C,Y,K,J,S,1,5,9,11,-16}      ........   (1)

Also    B∪A = {1,5,9,11,-16} ∩ {C,Y,K,J,S}

          = {C,Y,K,J,S,1,5,9,11,-16}    .......  (2)

 

From (1) and (2) we have, A∪B = B∪A for the give sets A,B.

Hence the commutative property of set unios verified.



9)  

 If A = {20, 40,60, 80 },  B = {24,40,48,72,96}  and C = {28,40,48,56,84,112} then find ,

verify whether A\(B\C) = (A\B)∖C. Justify your Answer.





Answer: 2




SOLUTION 1 :

Solution:

 B∖C = {24,40,48,72,96} /{28,40,48,56,84,112} 

B∖C  =  {24,72,96}

A∖(B∖C)  = {20, 40,60, 80 } /  {24,72,96}

A(B /C)   = {20, 40,60, 80 } ......(1)

Now

(AB) =  {20, 40,60, 80 }/ {24,40,48,72,96}

       =  {20,60,80}

thus (AB) /C = {20,60,80} / {28,40,48,56,84,112} 

(AB) /B =  {20,60,80}   .........(2)

Hence from (1) and (2), We have A (BC)    ≠   (AB) /C

Justification :

Since the sets A,B,C are not mutually disjoint, the set difference is not associative.



10)  

Given P = {4,6,7,9,-6},  Q = {4,-6,-3,-9,11} and R = {4,7,12,-6}.Find the  property of set intersection.





Answer: 3


SOLUTION 1 :

 Given ; 

P = {4,6,7,9,-6}

Q = {4,-6,-3,-9,11}

R = {4,7,-6,12}

To verify : 

Associative property of intersection of sets.

(ie,) P∩(Q∩R)  = (P∩R)∩R

verification : 

      L.H.S =  P∩(Q∩R)

Now,          Q∩R = {4,-6,-3,-9,11}∩{4,7,-6,12}

                 Q∩R = {4,-6}

     ∴  P∩(Q∩R) = {4,6,7,9,-6}∩{4,-6}

          P∩(Q∩R) = {4,-6}

    R.H.S = (P∩R)∩R

Now,       P∩Q = {4,6,7,9,-6}∩{4,-6,-3,-9,11}

               P∩Q = {4,-6}

  ∴ (P∩Q)∩R = {4,-6}∩{4,7,-6,12}  

         (P∩Q)∩R =  {4,-6}

From (1) and (2), we have

P∩(Q∩R)  = (P∩R)∩R