Q1Discrete Mathematics

Question

(a) Show that the relation $a \leq b$ on a set A = {1, 2, 3, 4} is reflexive. (b) Show that the relation on R defined by $a R b$ if and only if $a < b$ is not reflexive.

Answer 1

(a) A relation R on set A is mathematically reflexive if and only if $(a, a) \in R$ for every single element $a \in A$ . For the relation $a \leq b$ , since $a = a$ is universally true, $(a, a)$ is always valid. Thus, it is perfectly reflexive. (b) For the relation $a < b$ , the statement $a < a$ is fundamentally logically false for any number. Therefore, $(a, a) \in / R$ , proving it is not reflexive.

Q1Discrete Mathematics

Question

Answer