Let a relation 𝑅 on 𝑁 × 𝑁 be defined as: (𝑥1, 𝑦1)𝑅(𝑥2, 𝑦2) if and only if 𝑥1 ≤ 𝑥2 or 𝑦1 ≤ 𝑦2. Consider the two statements : (I) 𝑅 is reflexive but not symmetric. (II) 𝑅 is transitive Then which one of the following is true?

Question

Let a relation 𝑅 on 𝑁 × 𝑁 be defined as: (𝑥1, 𝑦1)𝑅(𝑥2, 𝑦2) if and only if𝑥1 ≤ 𝑥2 or 𝑦1 ≤ 𝑦2. Consider the two statements :(I) 𝑅 is reflexive but not symmetric.(II) 𝑅 is transitive which ...

Accepted Answer

(𝑥1, 𝑦1)𝑅(𝑥2, 𝑦2)⇒ 𝑥1 ≤ 𝑥2 or 𝑦1 ≤ 𝑦2 reflexive :(𝑥1, 𝑦1)(𝑥1, 𝑦1)⇒ 𝑥1 ≤ 𝑥1 or 𝑦1 ≤ 𝑦1 which is true. So, 𝑅 is reflexive. symmetric : (𝑥1, 𝑦1)(𝑥2, 𝑦2)⇒ 𝑥1 ≤ 𝑥2 or 𝑦1 ≤ 𝑦2⇒ 𝑥2 ≤ 𝑥1 or 𝑦2 ≤ 𝑦1 may or may not be true. For example (1,2) and (3,4)1 ≤ 3 and 2 ≤ 4 but 3 ¢ 1 and...

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