Let sets A space equals open curly brackets 1 comma space 2 comma space 3 comma space 4 close curly brackets and B space equals space open curly brackets 1 comma space left curly bracket 3 right curly bracket comma space 1 comma space left curly bracket 1 comma space 3 right curly bracket comma space left curly bracket 3 comma space 3 comma space 1 right curly bracket close curly brackets. Choose the contents of A space union space B and A space cross times space B in roster notation (removing duplicates).

(i) ={1,2,3,4,{3},{1,3}}

(ii)A X B ={(1,1), (1,{3}),(1,{1,3}),(2,1), (2,{3}),(2,{1,3}),(3,1), (3,{3}),(3,{1,3}),(4,1), (4,{3}),(4,{1,3})}

Step-By-Step Explanation:

A={1,2,3,4}

B={1,{3},1,{1,3},{3,3,1}}

Removing Duplicates: B={1,{3},{1,3}}

Definition : Given two non-empty sets A and B, the set of all ordered pairs (x, y), where x ∈ A and y ∈ B is called Cartesian product of A and B; symbolically, we write A × B = {(x, y) |  x ∈ A and y ∈ B}  

(i) ={1,2,3,4,{3},{1,3}}

(ii)A X B ={(1,1), (1,{3}),(1,{1,3}),(2,1), (2,{3}),(2,{1,3}),(3,1), (3,{3}),(3,{1,3}),(4,1), (4,{3}),(4,{1,3})}

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98