Question

Among the following, equal sets are [ ] A) E = {1, 0}, H = {a, b} B) A = {0, a}, C = {b, 0} C) D = {4, 8, 12}, F= {8, 12, 4} D) G = {1, 5, 7, 11}, I = {1, 2, 3, 4}

Answer 1

ANSWER

A={2,4,8,12}

n(A)=4

B={1,2,3,4}

 n(B)=4

C={4,8,12,14}

n(C)=4

D={3,1,4,2}

n(D)=4

E={−1,1}

n(E)=2

F={0,a}

n(F)=2

G={1,−1}

n(G)=2

H={0,1}

n(H)=2

Number of elements in A,B,C,D are same i.e. all have 4 elements. So ,they are comparable. 

Now, we see B and D has same elements.

So, B and D are equal sets.

Similarly, E,F,G, H are comparable as they all have same number of elements i.e. 2.

Clearly , E and G has same elements.

So, E and G are equal sets.

Answer 2

The answer is D = {4, 8, 12}, F= {8, 12, 4} are equal sets

Given:

A) E = {1, 0}  H = {a, b}

B) A = {0, a}, C = {b, 0}

C) D = {4, 8, 12}, F= {8, 12, 4}

D) G = {1, 5, 7, 11}, I = {1, 2, 3, 4}

To find: Equal sets in given sets

Solutions:

Equal Sets: The sets are which have same cardinal number and same elements are called as equal sets.

Example:  {a, b, c }  and {c, b, a}

                {2, 5, 8}  and  {5, 8, 2}    

A) E = {1, 0}  H = {a, b}  

⇒  n(E) = 2 and n(H) = 2

Here cardinal number of sets is equal but elements not same

⇒  E = {1, 0}  H = {a, b} are not equal sets  

B) A = {0, a}, C = {b, 0}

⇒  n(A) = 2 and n(C) = 2

Here cardinal number of sets is equal but elements not same

⇒  A = {0, a}, C = {b, 0}  are not equal sets

C) D = {4, 8, 12}, F= {8, 12, 4}

⇒ n(D) = 3 and n(F) = 3

Here cardinal number of sets is equal and elements are also equal

⇒ D = {4, 8, 12}, F= {8, 12, 4} are equal sets

D) G = {1, 5, 7, 11}, I = {1, 2, 3, 4}

⇒ n(G) = 4 and n(I) = 4

Here cardinal number of sets is equal but elements are not equal

G = {1, 5, 7, 11}, I = {1, 2, 3, 4} are not equal sets  

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