Question

Determine whether the given relation is reflexive, symmetric, transitive, or none of these. (Select all that apply.)

Let A be the set of all strings of 0's, 1's, and 2's that have length 4 and for which the sum of the characters in the string is less than or equal to 2. Define a relation R on A as follows:

For every s, t E A, s R t ⇔ the sum of the characters of s equals the sum of the characters of t.

A. Reflective
B. Symmetric
C. Transitive
D. Non of above

Answer 1

Reflective

Symmetric

Transitive

Explanation:

A is reflexive: Since the relation is based on the sum of characters in a string, s=s, so sAs.

A is symmetric: Suppose s and t are strings. if sAt, then s and t have the same sum of their characters, so tAs.

A is transitive: Suppose s,t and r are strings. if sAt, and tAr, then since s and t have the same sum, and t and r have the same sum, s and r have the same sum. So sAr.