In 9-33, determine whether the given is reflexive symmetric, transitive, or none of these. Justify your answer.
Let A be the set of all strings of a’s and b’s of length 4. Define a relation R on A as follows: For every
To justify whether the given relation is reflexive, symmetric, transitive, or none of these.
Given information:
Let A be the set of all strings of a’s and b’s of length 4. Define a relation R on A as follows: For all s, t ∈ A, s R t ⇔ s has the same first two characters as t.
Calculation:
Reflexive:
Suppose s is any string in A. then
Thus, reflexive
Symmetric:
Suppose s and t are any strings in A such that
By definition of R, s has the same first two characters as t.
Then t has the same first two characters as s, and so