Scroll:set and function >> De Morgans Law >> saq (4253)

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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.

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1)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {3,5,7,9,11,13,15,17} ,  B = {3,4,7,9} and  

C = {5,11,15,21,23} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) =



Answer:_______________




2)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {2,4,6,8,10,12,14,16} ,  B = {2,3,6,8} and  C = {4,10,14,23,25} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =  




Answer:_______________




3)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {2,4,6,8,10,12,14,16} ,  B = {2,3,6,8} and  

C = {4,10,14,24,26} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) =



Answer:_______________




4)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {4,6,8,10,12,14,16,18} ,  B = {4,5,8,10} and  C = {6,12,16,23,25} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =  




Answer:_______________




5)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {6,8,10,12,14,16,18,20} ,  B = {6,7,10,12} and  

C = {8,14,18,22,24} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) =



Answer:_______________




6)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {3,5,7,9,11,13,15,17} ,  B = {3,4,7,9} and  C = {5,11,15,25,27} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =  




Answer:_______________




7)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {3,5,7,9,11,13,15,17} ,  B = {3,4,7,9} and  

C = {5,11,15,22,24} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) =



Answer:_______________




8)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {5,7,9,11,13,15,17,19} ,  B = {5,6,9,11} and  C = {7,13,17,22,24} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =  




Answer:_______________




9)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {6,8,10,12,14,16,18,20} ,  B = {6,7,10,12} and  

C = {8,14,18,24,26} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) =



Answer:_______________




10)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {2,4,6,8,10,12,14,16} ,  B = {2,3,6,8} and  C = {4,10,14,25,27} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =  




Answer:_______________




 

1)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {3,5,7,9,11,13,15,17} ,  B = {3,4,7,9} and  

C = {5,11,15,21,23} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) = Answer: 3,5,7,9,11,13,15,17


SOLUTION 1 :

 Given ; 

A = {3,5,7,9,11,13,15,17} 

B = {3,4,7,9} 

C = {5,11,15,21,23} 

To Verify : 

De Morgans laws for set difference

A∖ (B∩C) = (A∖B)∪(A∖C)

Verifications : (i) A∖ (B∩C) = (A∖B)∪(A∖C)

L.H.S :   A∖ (B∩C) 

(B∩C) =  {3,4,7,9} ∪ {5,11,15,21,23} 

(B∩C) = { }

       A∖ (B∩C)  =  {3,5,7,9,11,13,15,17} âˆ– { }

      A∖ (B∩C) = {3,5,7,9,11,13,15,17}          ............   (i)

R.H.S = (A∖B)∪(A∖C)

A∖B =  {3,5,7,9,11,13,15,17} âˆ– {3,4,7,9} 

A∖B = {5,11,13,15,17}

A∖C = {3,5,7,9,11,13,15,17} âˆ– {5,11,15,21,23} 

A∖C = {3,7,9,13,17}

(A∖B)∪(A∖C) = {5,11,13,15,17} ∩ {3,7,9,13,17}

(A∖B)∪(A∖C) = {3,5,7,9,11,13,15,17}   .........    (2)

From (i) and (2) we get A∖ (B∩C) = (A∖B)∪(A∖C)

Hence verified        →                 {3,5,7,9,11,13,15,17}




2)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {2,4,6,8,10,12,14,16} ,  B = {2,3,6,8} and  C = {4,10,14,23,25} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =   Answer: 12,16


SOLUTION 1 :

  Given ; 

A = {2,4,6,8,10,12,14,16} 

B = {2,3,6,8} 

C = {4,10,14,23,25} 

To Verify : 

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

Verifications : (i)  A∖ (B∪C) = (A∖B) ∩ (A∖C)

L.H.S :   A∖ (B∪C) 

(B∪C) =  {2,3,6,8} ∪ {4,10,14,23,25} 

(B∪C) = {2,4,6,8,10,14,23,25}

A∖ (B∪C)  =  {2,4,6,8,10,12,14,16} âˆ– {2,3,4,6,8,10,14,23,25}

      A∖ (B∪C) = {12,16}          ............   (i)

R.H.S = (A∖B) ∩ (A∖C)

A∖B =  {2,4,6,8,10,12,14,16} âˆ– {2,3,6,8} 

A∖B = {4,10,12,14,16}

A∖C = {2,4,6,8,10,12,14,16} âˆ– {4,10,14,23,25} 

A∖C = {2,6,8,12,16}

(A∖B) ∩ (A∖C) = {4,10,12,14,16} ∩ {2,6,8,12,16}

(A∖B) ∩ (A∖C) = {12,16}    .........    (2)

From (i) and (2) we get A∖ (B∪C) = (A∖B) ∩ (A∖C)

Hence verified        →                 {12,16}




3)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {2,4,6,8,10,12,14,16} ,  B = {2,3,6,8} and  

C = {4,10,14,24,26} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) = Answer: 2,4,6,8,10,12,14,16


SOLUTION 1 :

 Given ; 

A = {2,4,6,8,10,12,14,16} 

B = {2,3,6,8} 

C = {4,10,14,24,26} 

To Verify : 

De Morgans laws for set difference

A∖ (B∩C) = (A∖B)∪(A∖C)

Verifications : (i) A∖ (B∩C) = (A∖B)∪(A∖C)

L.H.S :   A∖ (B∩C) 

(B∩C) =  {2,3,6,8} ∪ {4,10,14,24,26} 

(B∩C) = { }

       A∖ (B∩C)  =  {2,4,6,8,10,12,14,16} âˆ– { }

      A∖ (B∩C) = {2,4,6,8,10,12,14,16}          ............   (i)

R.H.S = (A∖B)∪(A∖C)

A∖B =  {2,4,6,8,10,12,14,16} âˆ– {2,3,6,8} 

A∖B = {4,10,12,14,16}

A∖C = {2,4,6,8,10,12,14,16} âˆ– {4,10,14,24,26} 

A∖C = {2,6,8,12,16}

(A∖B)∪(A∖C) = {4,10,12,14,16} ∩ {2,6,8,12,16}

(A∖B)∪(A∖C) = {2,4,6,8,10,12,14,16}   .........    (2)

From (i) and (2) we get A∖ (B∩C) = (A∖B)∪(A∖C)

Hence verified        →                 {2,4,6,8,10,12,14,16}




4)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {4,6,8,10,12,14,16,18} ,  B = {4,5,8,10} and  C = {6,12,16,23,25} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =   Answer: 14,18


SOLUTION 1 :

  Given ; 

A = {4,6,8,10,12,14,16,18} 

B = {4,5,8,10} 

C = {6,12,16,23,25} 

To Verify : 

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

Verifications : (i)  A∖ (B∪C) = (A∖B) ∩ (A∖C)

L.H.S :   A∖ (B∪C) 

(B∪C) =  {4,5,8,10} ∪ {6,12,16,23,25} 

(B∪C) = {4,6,8,10,12,16,23,25}

A∖ (B∪C)  =  {4,6,8,10,12,14,16,18} âˆ– {4,5,6,8,10,12,16,23,25}

      A∖ (B∪C) = {14,18}          ............   (i)

R.H.S = (A∖B) ∩ (A∖C)

A∖B =  {4,6,8,10,12,14,16,18} âˆ– {4,5,8,10} 

A∖B = {6,12,14,16,18}

A∖C = {4,6,8,10,12,14,16,18} âˆ– {6,12,16,23,25} 

A∖C = {4,8,10,14,18}

(A∖B) ∩ (A∖C) = {6,12,14,16,18} ∩ {4,8,10,14,18}

(A∖B) ∩ (A∖C) = {14,18}    .........    (2)

From (i) and (2) we get A∖ (B∪C) = (A∖B) ∩ (A∖C)

Hence verified        →                 {14,18}




5)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {6,8,10,12,14,16,18,20} ,  B = {6,7,10,12} and  

C = {8,14,18,22,24} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) = Answer: 6,8,10,12,14,16,18,20


SOLUTION 1 :

 Given ; 

A = {6,8,10,12,14,16,18,20} 

B = {6,7,10,12} 

C = {8,14,18,22,24} 

To Verify : 

De Morgans laws for set difference

A∖ (B∩C) = (A∖B)∪(A∖C)

Verifications : (i) A∖ (B∩C) = (A∖B)∪(A∖C)

L.H.S :   A∖ (B∩C) 

(B∩C) =  {6,7,10,12} ∪ {8,14,18,22,24} 

(B∩C) = { }

       A∖ (B∩C)  =  {6,8,10,12,14,16,18,20} âˆ– { }

      A∖ (B∩C) = {6,8,10,12,14,16,18,20}          ............   (i)

R.H.S = (A∖B)∪(A∖C)

A∖B =  {6,8,10,12,14,16,18,20} âˆ– {6,7,10,12} 

A∖B = {8,14,16,18,20}

A∖C = {6,8,10,12,14,16,18,20} âˆ– {8,14,18,22,24} 

A∖C = {6,10,12,16,20}

(A∖B)∪(A∖C) = {8,14,16,18,20} ∩ {6,10,12,16,20}

(A∖B)∪(A∖C) = {6,8,10,12,14,16,18,20}   .........    (2)

From (i) and (2) we get A∖ (B∩C) = (A∖B)∪(A∖C)

Hence verified        →                 {6,8,10,12,14,16,18,20}




6)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {3,5,7,9,11,13,15,17} ,  B = {3,4,7,9} and  C = {5,11,15,25,27} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =   Answer: 13,17


SOLUTION 1 :

  Given ; 

A = {3,5,7,9,11,13,15,17} 

B = {3,4,7,9} 

C = {5,11,15,25,27} 

To Verify : 

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

Verifications : (i)  A∖ (B∪C) = (A∖B) ∩ (A∖C)

L.H.S :   A∖ (B∪C) 

(B∪C) =  {3,4,7,9} ∪ {5,11,15,25,27} 

(B∪C) = {3,5,7,9,11,15,25,27}

A∖ (B∪C)  =  {3,5,7,9,11,13,15,17} âˆ– {3,4,5,7,9,11,15,25,27}

      A∖ (B∪C) = {13,17}          ............   (i)

R.H.S = (A∖B) ∩ (A∖C)

A∖B =  {3,5,7,9,11,13,15,17} âˆ– {3,4,7,9} 

A∖B = {5,11,13,15,17}

A∖C = {3,5,7,9,11,13,15,17} âˆ– {5,11,15,25,27} 

A∖C = {3,7,9,13,17}

(A∖B) ∩ (A∖C) = {5,11,13,15,17} ∩ {3,7,9,13,17}

(A∖B) ∩ (A∖C) = {13,17}    .........    (2)

From (i) and (2) we get A∖ (B∪C) = (A∖B) ∩ (A∖C)

Hence verified        →                 {13,17}




7)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {3,5,7,9,11,13,15,17} ,  B = {3,4,7,9} and  

C = {5,11,15,22,24} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) = Answer: 3,5,7,9,11,13,15,17


SOLUTION 1 :

 Given ; 

A = {3,5,7,9,11,13,15,17} 

B = {3,4,7,9} 

C = {5,11,15,22,24} 

To Verify : 

De Morgans laws for set difference

A∖ (B∩C) = (A∖B)∪(A∖C)

Verifications : (i) A∖ (B∩C) = (A∖B)∪(A∖C)

L.H.S :   A∖ (B∩C) 

(B∩C) =  {3,4,7,9} ∪ {5,11,15,22,24} 

(B∩C) = { }

       A∖ (B∩C)  =  {3,5,7,9,11,13,15,17} âˆ– { }

      A∖ (B∩C) = {3,5,7,9,11,13,15,17}          ............   (i)

R.H.S = (A∖B)∪(A∖C)

A∖B =  {3,5,7,9,11,13,15,17} âˆ– {3,4,7,9} 

A∖B = {5,11,13,15,17}

A∖C = {3,5,7,9,11,13,15,17} âˆ– {5,11,15,22,24} 

A∖C = {3,7,9,13,17}

(A∖B)∪(A∖C) = {5,11,13,15,17} ∩ {3,7,9,13,17}

(A∖B)∪(A∖C) = {3,5,7,9,11,13,15,17}   .........    (2)

From (i) and (2) we get A∖ (B∩C) = (A∖B)∪(A∖C)

Hence verified        →                 {3,5,7,9,11,13,15,17}




8)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {5,7,9,11,13,15,17,19} ,  B = {5,6,9,11} and  C = {7,13,17,22,24} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =   Answer: 15,19


SOLUTION 1 :

  Given ; 

A = {5,7,9,11,13,15,17,19} 

B = {5,6,9,11} 

C = {7,13,17,22,24} 

To Verify : 

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

Verifications : (i)  A∖ (B∪C) = (A∖B) ∩ (A∖C)

L.H.S :   A∖ (B∪C) 

(B∪C) =  {5,6,9,11} ∪ {7,13,17,22,24} 

(B∪C) = {5,7,9,11,13,17,22,24}

A∖ (B∪C)  =  {5,7,9,11,13,15,17,19} âˆ– {5,6,7,9,11,13,17,22,24}

      A∖ (B∪C) = {15,19}          ............   (i)

R.H.S = (A∖B) ∩ (A∖C)

A∖B =  {5,7,9,11,13,15,17,19} âˆ– {5,6,9,11} 

A∖B = {7,13,15,17,19}

A∖C = {5,7,9,11,13,15,17,19} âˆ– {7,13,17,22,24} 

A∖C = {5,9,11,15,19}

(A∖B) ∩ (A∖C) = {7,13,15,17,19} ∩ {5,9,11,15,19}

(A∖B) ∩ (A∖C) = {15,19}    .........    (2)

From (i) and (2) we get A∖ (B∪C) = (A∖B) ∩ (A∖C)

Hence verified        →                 {15,19}




9)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {6,8,10,12,14,16,18,20} ,  B = {6,7,10,12} and  

C = {8,14,18,24,26} .

De Morgans laws for set difference

(i) A∖ (B∩C) = (A∖B)∪(A∖C)

(A∖B)∪(A∖C) = Answer: 6,8,10,12,14,16,18,20


SOLUTION 1 :

 Given ; 

A = {6,8,10,12,14,16,18,20} 

B = {6,7,10,12} 

C = {8,14,18,24,26} 

To Verify : 

De Morgans laws for set difference

A∖ (B∩C) = (A∖B)∪(A∖C)

Verifications : (i) A∖ (B∩C) = (A∖B)∪(A∖C)

L.H.S :   A∖ (B∩C) 

(B∩C) =  {6,7,10,12} ∪ {8,14,18,24,26} 

(B∩C) = { }

       A∖ (B∩C)  =  {6,8,10,12,14,16,18,20} âˆ– { }

      A∖ (B∩C) = {6,8,10,12,14,16,18,20}          ............   (i)

R.H.S = (A∖B)∪(A∖C)

A∖B =  {6,8,10,12,14,16,18,20} âˆ– {6,7,10,12} 

A∖B = {8,14,16,18,20}

A∖C = {6,8,10,12,14,16,18,20} âˆ– {8,14,18,24,26} 

A∖C = {6,10,12,16,20}

(A∖B)∪(A∖C) = {8,14,16,18,20} ∩ {6,10,12,16,20}

(A∖B)∪(A∖C) = {6,8,10,12,14,16,18,20}   .........    (2)

From (i) and (2) we get A∖ (B∩C) = (A∖B)∪(A∖C)

Hence verified        →                 {6,8,10,12,14,16,18,20}




10)  

 Verify De Morgans laws for set difference using the sets given below : (ple use ,)

A = {2,4,6,8,10,12,14,16} ,  B = {2,3,6,8} and  C = {4,10,14,25,27} .

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

(A∖B) ∩ (A∖C) =   Answer: 12,16


SOLUTION 1 :

  Given ; 

A = {2,4,6,8,10,12,14,16} 

B = {2,3,6,8} 

C = {4,10,14,25,27} 

To Verify : 

De Morgans laws for set difference

(i) A∖ (B∪C) = (A∖B) ∩ (A∖C)

Verifications : (i)  A∖ (B∪C) = (A∖B) ∩ (A∖C)

L.H.S :   A∖ (B∪C) 

(B∪C) =  {2,3,6,8} ∪ {4,10,14,25,27} 

(B∪C) = {2,4,6,8,10,14,25,27}

A∖ (B∪C)  =  {2,4,6,8,10,12,14,16} âˆ– {2,3,4,6,8,10,14,25,27}

      A∖ (B∪C) = {12,16}          ............   (i)

R.H.S = (A∖B) ∩ (A∖C)

A∖B =  {2,4,6,8,10,12,14,16} âˆ– {2,3,6,8} 

A∖B = {4,10,12,14,16}

A∖C = {2,4,6,8,10,12,14,16} âˆ– {4,10,14,25,27} 

A∖C = {2,6,8,12,16}

(A∖B) ∩ (A∖C) = {4,10,12,14,16} ∩ {2,6,8,12,16}

(A∖B) ∩ (A∖C) = {12,16}    .........    (2)

From (i) and (2) we get A∖ (B∪C) = (A∖B) ∩ (A∖C)

Hence verified        →                 {12,16}