Use the sets A 5 6 7 8 9 10 B g h i j C c d e f and D j

Use the sets A = {5, 6, 7, 8, 9, 10}, B = {g, h, i, j}, C = {c, d, e, f}, and D = {j, i, g, h} to answer the following problem. Which sets are equivalent but not equal? (Select all that apply.) A and B A and C A and D B and C B and D C and D none of these

Solution

Given that

A = { 5 , 6 , 7 , 8 , 9 , 10 } , B = { g , h , i , j } , C = { c , d , e , f } , D = { j , i , g , h }

We know that

If two sets contain same elements they are said to be equal sets

If cardinality of two sets are same then they are said to be equivalent sets

Cardinality of set is defined as number of elements in given set

Hence ,

   B = { g , h , i , j } , C = { c , d , e , f }

Cardinality of B = 4 , Cardinality of C = 4

Hence ,

B and C are equivalent sets

B and C does not have same elements

B and C are not equal sets

Therefore ,

B and C are equivalent but not equal

C = { c , d , e , f } , D = { j , i , g , h }

Cardinality of C = 4 , Cardinality of D = 4

Hence ,

C and D are equivalent sets

C and D not have same elements

C and D are not equal sets

Therefore ,

C and D are equivalent but not equal

Finally

  B and C are equivalent but not equal

   C and D are equivalent but not equal