In our daily life we usually talk about relations between various things. For example, we say someone is the father of another person, 5 is greater than 3, Paris is the capital city of France, etc..

1. Let A = { 1, 2, 4, 6, 7} and B = { 5, 12, 7, 9, 8, 3}
List all ordered pairs (x, y) which satisfy each of the following sentences where x∈A, y∈B.

(a) x is greater than y
(b) y is a multiple of x
(c) The sum of x and y is odd
(d) x is half of y

2. Let A = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
List all ordered pairs (x, y) which satisfy each of the following sentences,
where x, y∈A.

(a) y is a multiple of x
(b) x is the square of y
(c) x is less than y
(d) x is a prime factor of y

Let U = {x: x is a student in your class}
(i) In each of the following, list all ordered pairs (x, y) which satisfy the given sentence
where x, y ∈ U.

(a) x is taller than y
(b) x is younger than y

(ii) Discuss other ways that you can relate the students in your class.

As you have noticed from the above Activity, each sentence involves what is intuitively understood to be a relationship. Expressions of the type “is greater than”, “is multiple of”, “is a factor of”, “is taller than”, etc. which express the relation are referred to as relating phrases.