Question

Classify the following sets which are equivalent but not equal sets.

$G=\left\{alltheoddnumbersfrom1to51\right\};H=\left\{alllettersofenglishalphabet\right\}$

Answer 1

Equivalent but not equal

$G=\left\{alltheoddnumbersfrom1to51\right\};H=\left\{alllettersofenglishalphabet\right\}$

$G=\left\{1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51\right\}$, $H=\left\{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z.\right\}$

No. of elements in each set is 26, therefore it is Equivalent

But no element is common and hence not equal.

Equal sets: Two sets are equal if they have the same elements. If set A and B are equal, then A=B otherwise A≠B.

Equivalent sets: Two finite sets are said to be equivalent if the number of distinct elements in both sets is equal. If sets A and B are equivalent, we write as A↔B.