R = {(a, b) | length of string a = length of string b} on the set of strings of English letters. Prove that R is an equivalence relation.

To prove that R is an equivalence relation, we need to show that it satisfies three conditions: reflexivity, symmetry, and transitivity.

1. Reflexivity: For all strings a, we have (a, a) ∈ R. This is true because the length of a string is always equal to the length of itself.
2. Symmetry: For all strings a and b, if (a, b) ∈ R, then (b, a) ∈ R. This is true because if the length of string a is equal to the length of string b, then the length of string b is also equal to the length of string a.
3. Transitivity: For all strings a, b, and c, if (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R. This is true because if the length of string a is equal to the length of string b, and the length of string b is equal to the length of string c, then the length of string a is also equal to the length of string c.

Therefore, R is reflexive, symmetric, and transitive, and is therefore an equivalence relation.

R={(a,b)∣ length of string a=length of string b}