Sasi Math (Revised for 1024)

Scroll:set and function >> set and function >> ps (4152)

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.

Give A = {T,V,R,Q,E,3,6,8,7} B = {3,12,6,-7,V,R,Q,E} very the property of set intersection.

1) Associative
2) Commutative
3) none of above
4) Distributive

Answer:_______________

Given P = {3,5,8,9,-6}, Q = {3,-6,-2,-10,9} and R = {3,8,13,-6}.Find the property of set intersection.

1) Associative
2) Commutative
3) none of above
4) Distributive

Answer:_______________

If A = {5, 10,15, 20 }, B = {6,10,12,18,24} and C = {7,10,12,14,21,28} then find ,

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

1) commutative
2) associative
3) equal
4) not associative

Answer:_______________

Give A = {T,I,G,O,M}, B = {3,5,9,11,-17} very the property of set union.

1) none of above
2) Associative
3) Distributive
4) Commutative

Answer:_______________

Give A = {W,O,J,B,G,3,7,8,7} B = {3,10,7,-7,O,J,B,G} very the property of set intersection.

1) Associative
2) Commutative
3) none of above
4) Distributive

Answer:_______________

Given P = {3,5,8,9,-8}, Q = {3,-8,-4,-9,11} and R = {3,8,14,-8}.Find the property of set intersection.

1) Distributive
2) none of above
3) Associative
4) Commutative

Answer:_______________

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.

1) not associative
2) equal
3) commutative
4) associative

Answer:_______________

Give A = {W,Z,T,C,O}, B = {2,5,9,11,-15} very the property of set union.

1) Distributive
2) none of above
3) Associative
4) Commutative

Answer:_______________

Give A = {J,A,D,D,J,4,5,8,7} B = {4,13,5,-5,A,D,D,J} very the property of set intersection.

1) none of above
2) Commutative
3) Associative
4) Distributive

Answer:_______________

10)

Given P = {3,6,8,9,-6}, Q = {3,-6,-4,-9,9} and R = {3,8,12,-6}.Find the property of set intersection.

1) Distributive
2) none of above
3) Associative
4) Commutative

Answer:_______________

Give A = {B,U,O,I,B,3,6,8,7} B = {3,12,6,-7,U,O,I,B} very the property of set intersection.

1) Distributive
2) Commutative
3) none of above
4) Associative

Answer: 2

SOLUTION 1 :

Now A∩B = {B,U,O,I,B,3,6,8,7} ∩ {3,12,6,-7,U,O,I,B}

= {U,O,I,3,6} ........ (1)

Also B∩A = {3,12,6,-7,U,O,I,B} ∩ {B,U,O,I,B,3,6,8,7}

= {U,O,I,3,6} ....... (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.

Given P = {3,5,8,9,-6}, Q = {3,-6,-2,-10,9} and R = {3,8,13,-6}.Find the property of set intersection.

1) none of above
2) Distributive
3) Commutative
4) Associative

Answer: 4

SOLUTION 1 :

Given ;

P = {3,5,8,9,-6}

Q = {3,-6,-2,-10,9}

R = {3,8,-6,13}

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,-6,-2,-10,9}∩{3,8,-6,13}

Q∩R = {3,-6}

∴ P∩(Q∩R) = {3,5,8,9,-6}∩{3,-6}

P∩(Q∩R) = {3,-6}

R.H.S = (P∩R)∩R

Now, P∩Q = {3,5,8,9,-6}∩{3,-6,-2,-10,9}

P∩Q = {3,-6}

∴ (P∩Q)∩R = {3,-6}∩{3,8,-6,13}

(P∩Q)∩R = {3,-6}

From (1) and (2), we have

P∩(Q∩R) = (P∩R)∩R

If A = {5, 10,15, 20 }, B = {6,10,12,18,24} and C = {7,10,12,14,21,28} then find ,

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

1) commutative
2) equal
3) not associative
4) associative

Answer: 3

SOLUTION 1 :

Solution:

Bâˆ–C = {6,10,12,18,24} /{7,10,12,14,21,28}

Bâˆ–C = {6,18,24}

Aâˆ–(Bâˆ–C) = {5, 10,15, 20 } / {6,18,24}

$\frac{A}{(B}$ /C) = {5, 10,15, 20 } ......(1)

Now

$\frac{(A}{B)}$ = {5, 10,15, 20 }/ {6,10,12,18,24}

= {5,15,20}

thus $\frac{(A}{B)}$ /C = {5,15,20} / {7,10,12,14,21,28}

$\frac{(A}{B)}$ /B = {5,15,20} .........(2)

Hence from (1) and (2), We have A $\frac{(B}{C)}$ ≠ $\frac{(A}{B)}$ /C

Justification :

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

Give A = {I,O,E,N,T}, B = {3,5,9,11,-17} very the property of set union.

1) Distributive
2) none of above
3) Associative
4) Commutative

Answer: 4

SOLUTION 1 :

Now A∪B = {I,O,E,N,T} ∪ {3,5,9,11,-17}

= {I,O,E,N,T,3,5,9,11,-17} ........ (1)

Also B∪A = {3,5,9,11,-17} ∩ {I,O,E,N,T}

= {I,O,E,N,T,3,5,9,11,-17} ....... (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.

Give A = {T,R,C,L,D,3,7,8,7} B = {3,10,7,-7,R,C,L,D} very the property of set intersection.

1) Distributive
2) Commutative
3) Associative
4) none of above

Answer: 2

SOLUTION 1 :

Now A∩B = {T,R,C,L,D,3,7,8,7} ∩ {3,10,7,-7,R,C,L,D}

= {R,C,L,3,7} ........ (1)

Also B∩A = {3,10,7,-7,R,C,L,D} ∩ {T,R,C,L,D,3,7,8,7}

= {R,C,L,3,7} ....... (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.

Given P = {3,5,8,9,-8}, Q = {3,-8,-4,-9,11} and R = {3,8,14,-8}.Find the property of set intersection.

1) none of above
2) Distributive
3) Commutative
4) Associative

Answer: 4

SOLUTION 1 :

Given ;

P = {3,5,8,9,-8}

Q = {3,-8,-4,-9,11}

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

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,-8,-4,-9,11}∩{3,8,-8,14}

Q∩R = {3,-8}

∴ P∩(Q∩R) = {3,5,8,9,-8}∩{3,-8}

P∩(Q∩R) = {3,-8}

R.H.S = (P∩R)∩R

Now, P∩Q = {3,5,8,9,-8}∩{3,-8,-4,-9,11}

P∩Q = {3,-8}

∴ (P∩Q)∩R = {3,-8}∩{3,8,-8,14}

(P∩Q)∩R = {3,-8}

From (1) and (2), we have

P∩(Q∩R) = (P∩R)∩R

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.

1) commutative
2) associative
3) not associative
4) equal

Answer: 3

SOLUTION 1 :

Solution:

Bâˆ–C = {24,40,48,72,96} /{28,40,48,56,84,112}

Bâˆ–C = {24,72,96}

Aâˆ–(Bâˆ–C) = {20, 40,60, 80 } / {24,72,96}

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

Now

$\frac{(A}{B)}$ = {20, 40,60, 80 }/ {24,40,48,72,96}

= {20,60,80}

thus $\frac{(A}{B)}$ /C = {20,60,80} / {28,40,48,56,84,112}

$\frac{(A}{B)}$ /B = {20,60,80} .........(2)

Hence from (1) and (2), We have A $\frac{(B}{C)}$ ≠ $\frac{(A}{B)}$ /C

Justification :

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

Give A = {S,H,E,V,F}, B = {2,5,9,11,-15} very the property of set union.

1) Distributive
2) Commutative
3) Associative
4) none of above

Answer: 2

SOLUTION 1 :

Now A∪B = {S,H,E,V,F} ∪ {2,5,9,11,-15}

= {S,H,E,V,F,2,5,9,11,-15} ........ (1)

Also B∪A = {2,5,9,11,-15} ∩ {S,H,E,V,F}

= {S,H,E,V,F,2,5,9,11,-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.

Give A = {M,P,L,N,A,4,5,8,7} B = {4,13,5,-5,P,L,N,A} very the property of set intersection.

1) none of above
2) Commutative
3) Distributive
4) Associative

Answer: 2

SOLUTION 1 :

Now A∩B = {M,P,L,N,A,4,5,8,7} ∩ {4,13,5,-5,P,L,N,A}

= {P,L,N,4,5} ........ (1)

Also B∩A = {4,13,5,-5,P,L,N,A} ∩ {M,P,L,N,A,4,5,8,7}

= {P,L,N,4,5} ....... (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.

10)

Given P = {3,6,8,9,-6}, Q = {3,-6,-4,-9,9} and R = {3,8,12,-6}.Find the property of set intersection.

1) Associative
2) Distributive
3) Commutative
4) none of above

Answer: 1

SOLUTION 1 :

Given ;

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

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

R = {3,8,-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 = {3,-6,-4,-9,9}∩{3,8,-6,12}

Q∩R = {3,-6}

∴ P∩(Q∩R) = {3,6,8,9,-6}∩{3,-6}

P∩(Q∩R) = {3,-6}

R.H.S = (P∩R)∩R

Now, P∩Q = {3,6,8,9,-6}∩{3,-6,-4,-9,9}

P∩Q = {3,-6}

∴ (P∩Q)∩R = {3,-6}∩{3,8,-6,12}

(P∩Q)∩R = {3,-6}

From (1) and (2), we have

P∩(Q∩R) = (P∩R)∩R