Question

From the sets given below, select equal set:
\[
  A = \left\{ {2,4,8,12} \right\}, \\
  B = \left\{ {1,2,3,4} \right\}, \\
  C = \left\{ {4,8,12,14} \right\}, \\
  D = \left\{ {3,1,4,2} \right\}, \\
  E = \left\{ { - 1,1} \right\}, \\
  F = \left\{ {0,a} \right\}, \\
  G = \left\{ { - 1,1} \right\}, \\
  H = \left\{ {0,1} \right\} \\
\]

Answer 1

Hint: Compare the sets having equal number of elements.

For the given sets, we have:
\[
  A = \left\{ {2,4,8,12} \right\} \\
  n\left( A \right) = 4 \\
  B = \left\{ {1,2,3,4} \right\} \\
  n\left( B \right) = 4 \\
  C = \left\{ {4,8,12,14} \right\} \\
  n\left( C \right) = 4 \\
  D = \left\{ {3,1,4,2} \right\} \\
  n\left( D \right) = 4 \\
  E = \left\{ { - 1,1} \right\} \\
  n\left( E \right) = 2 \\
  F = \left\{ {0,a} \right\} \\
  n\left( F \right) = 2 \\
  G = \left\{ { - 1,1} \right\} \\
  n\left( G \right) = 2 \\
  H = \left\{ {0,1} \right\} \\
  n\left( H \right) = 2 \\
\]
Number of elements in A, B, C, D are the same i.e. all have 4 elements. So, they are comparable.
Now we see that B and D have the same elements.
So, B and D are equal sets.
Similarly E, F, G and H are comparable as they all have same number of elements i.e. 2
Clearly, E and G have the same elements.
So, E and G are equal sets.

Note: We need to remember that 2 sets can be equal if and only if they are comparable or the number of elements in both of the sets is the same. Even if some of the elements in two sets are equal, still they cannot be equal till they have equal no of elements.