Question

The pre-image of each element of Y in X _________ (exists/does not exist). So, the function is ________ (onto/not onto).​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The pre-image of each element of Y in X exists. So, the function is onto.

• Let us consider two sets, Set A and Set B, which consist of elements. If for every element in B, there is at least one element matching with A, then the function is said to be onto function.  
• In the given question for every element in set Y, there exists a pre-image in set X. This means that every element in X will have a complementary element in Y.
• Conversely, if we had chosen the option 'does not exist' in the first sentence, it would be concluded that the function is not onto.

Thus, the pre-image of each element of Y in X exists. So, the function is onto.​