On (A={1,2,3,4,5}), (R={(a,b):a) and (b) are both less than (5)(}). Is this relation transitive?

Correct answer: Yes, it is transitive

Step 1: If ((a,b)) is in the relation, then both (a) and (b) are less than (5). If ((b,c)) is also in the relation, then both (b) and (c) are less than (5). Step 2: Hence (a) and (c) are both less than (5), so ((a,c)) is in the relation. Step 3: For property-based relations, check whether the first and third elements keep the property.