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Consider the following statements in respect of relations and functions: 1. All relations are functions but all functions are not relations. 2. A relation from A to B is a subset of Cartesian product A × B. 3. A relation in A is a subset of Cartesian product A × A. Which of the above statements are correct?

Consider the following statements in respect of relations and functions: 1. All relations are functions but all functions are not relations. 2. A relation from A to B is a subset of Cartesian product A × B. 3. A relation in A is a subset of Cartesian product A × A. Which of the above statements are correct? Correct Answer 2 and 3 only

Explanation:

Statement:1. All relations are functions but all functions are not relations.

All functions are relations, but not all relations are functions. A function

is a relation that for each input, there is only one output.

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So, statement 1 is incorrect.

Statement: 2.  A relation from A to B is a subset of Cartesian product A × B.

If A and B are set, the Cartesian product of A and B is the set

A × B = {(a, b) : (a ∈ A) and (b ∈ B)}.

Every relation is a subset of the Cartesian product

So, statement 2 is correct.

Statement: 3. A relation in A is a subset of Cartesian product A × A.

A relation from a non-empty set A to a non-empty set A is a subset of

cartesian product A × A. The first element is called the preimage of the

second and the second element is called the image of the first.

So, statement 3 is correct.

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