1.

Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}. Find: i. A – B ii. A – C iii. A – D iv. B – A v. C – A vi. D – A vii. B – C viii. B – D

Answer»

A – B is defined as {x ϵ A : x ∉ B} 

i. A – B is defined as {x ϵ A : x ∉ B} 

A = {3, 6, 12, 15, 18, 21} 

B = {4, 8, 12, 16, 20} 

A – B = {3, 6, 15, 18, 21} 

ii. A – C is defined as {x ϵ A : x ∉ C} 

A = {3, 6, 12, 15, 18, 21} 

C = {2, 4, 6, 8, 10, 12, 14, 16} 

A – C = {3, 15, 18, 21} 

iii. A – D is defined as {x ϵ A : x ∉ D} 

A = {3, 6, 12, 15, 18, 21} 

D = {5, 10, 15, 20}. 

A – D = {3, 6, 12, 18, 21} 

iv. B – A is defined as {x ϵ B : x ∉ A} 

A = {3, 6, 12, 15, 18, 21} 

B = {4, 8, 12, 16, 20} 

B – A = {4, 8, 16, 20} 

v. C – A is defined as {x ϵ C : x ∉ A} 

A = {3, 6, 12, 15, 18, 21} 

C = {2, 4, 6, 8, 10, 12, 14, 16} 

C – A = {2, 4, 8, 10, 14, 16} 

vi. D – A is defined as {x ϵ D : x ∉ A} 

A = {3, 6, 12, 15, 18, 21} 

D = {5, 10, 15, 20}. 

D – A = {5, 10, 20}. 

vii. B – C is defined as {x ϵ B : x ∉ C} 

B = {4, 8, 12, 16, 20} 

C = {2, 4, 6, 8, 10, 12, 14, 16} 

B – C = {4, 8, 20} 

viii. B – D is defined as {x ϵ B : x ∉ D} 

B = {4, 8, 12, 16, 20} 

D = {5, 10, 15, 20} 

B – D = {4, 8, 12, 16}



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