Word Problems Based on Relations

Word problems often describe connections using everyday language. The goal is to translate these descriptions into ordered pairs. Once written as a relation, it becomes easier to analyse, interpret, or present the information using tables, lists, or diagrams.

First, decide which sets are involved. A word problem usually mentions two groups of objects: people, numbers, cities, items, or options. These become the sets A and B.

Look for statements that show how one item connects to another. Each connection becomes an ordered pair (a,b). This is the heart of converting a word problem into a relation.

Problem: Three children {A, B, C} choose from two fruits {apple, banana}. A and C choose apple, and B chooses banana.

Problem: Cities {P, Q, R} and distances: P is connected to Q, Q to R, and P to R.

Problem: In the set {1,2,3,4,6}, write the relation “a divides b”.

Problem: In a group {A, B, C}, A is friends with B, and B is friends with C. The relation is one-way (not symmetric) because friendship here means A follows B on a website.

Problem: In a list {x, y, z}, x comes before y, and y comes before z.

Word problems strengthen the ability to convert real situations into precise mathematical descriptions. Once written as ordered pairs, relations become easier to represent using tables, digraphs, and matrices, and to analyse for properties like symmetry, reflexivity, or transitivity.