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Which of the following is not true?
  • a)
    Every relation from the set A to the set B is a function from the set A to the set B.
  • b)
    If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where a is called the pre-image of b under f.
  • c)
    Every function from the set A to the set B is a relation from the set A to the set B
  • d)
    If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where b is called the image of a under f.
Correct answer is option 'A'. Can you explain this answer?
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Which of the following is not true?a)Every relation from the set A to ...
A relation f from a set A to a set B is said to be function if every element of set A has one and only one image in set B. In other words, a function f is a relation such that no two pairs in the relation has the same first element. The notation f : X →Y means that f is a function from X to Y.
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Which of the following is not true?a)Every relation from the set A to ...
As we know that function is a unique case of relation between two sets where "all" elements of domain should have one and only one image in the codomain.
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Which of the following is not true?a)Every relation from the set A to ...
Explanation:

a) Every relation from the set A to the set B is a function from the set A to the set B:
This statement is not true. A relation from set A to set B is a subset of the Cartesian product A x B, which means it can contain multiple ordered pairs with the same first element. In a function, each element of set A has a unique mapping to an element in set B, so there can't be multiple ordered pairs with the same first element. Therefore, a relation may not always be a function.

b) If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where a is called the pre-image of b under f:
This statement is true. In a function, if (a, b) ∈ f, it means that the element 'a' in set A is mapped to the element 'b' in set B. So, f(a) = b, where 'a' is called the pre-image of 'b' under f.

c) Every function from the set A to the set B is a relation from the set A to the set B:
This statement is true. A function is a special type of relation where each element in set A is mapped to a unique element in set B. Since a function is a relation, this statement is true.

d) If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where b is called the image of a under f:
This statement is true. In a function, if (a, b) ∈ f, it means that the element 'a' in set A is mapped to the element 'b' in set B. So, f(a) = b, where 'b' is called the image of 'a' under f.

Therefore, the statement that is not true is option a) Every relation from the set A to the set B is a function from the set A to the set B.
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Which of the following is not true?a)Every relation from the set A to the set B is a function from the set A to the set B.b)If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where a is called the pre-image of b under f.c)Every function from the set A to the set B is a relation from the set A to the set Bd)If f is a function from A to B and (a, b) ∈ f, then f(a) = b, where b is called the image of a under f.Correct answer is option 'A'. Can you explain this answer?
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