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SAT Exam  >  SAT Questions  >  Let P = {10, 20, 30} and Q = {5, 10, 15, 20}.... Start Learning for Free
Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the following functions is one – one and not onto?
  • a)
    f = {(10, 5), (10, 10), (10, 15), (10, 20)}
  • b)
    f = {(10, 5), (20, 10), (30, 15)}
  • c)
    f = {(20, 5), (20, 10), (30, 10)}
  • d)
    f = {(10, 5), (10, 10), (20, 15), (30, 20)}
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the followi...
The function f = {(10, 5), (20, 10), (30, 15)} is one-one and not onto. The function is one-one because element is set P = {10, 20, 30} has a distinct image in set Q = {5, 10, 15, 20}. The function is not onto because every element in set Q = {5, 10, 15, 20} does not have a pre-image in set P = {10, 20, 30} (20 does not have a pre-image in set P).
f = {(10, 5), (10, 10), (10, 15), (10, 20)} and f = {(10, 5), (10, 10), (20, 15), (30, 20)} are many – one onto.
f = {(20, 5), (20, 10), (30, 10)} is neither one – one nor onto.
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Most Upvoted Answer
Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the followi...
The function f = {(10, 5), (20, 10), (30, 15)} is one-one and not onto. The function is one-one because element is set P = {10, 20, 30} has a distinct image in set Q = {5, 10, 15, 20}. The function is not onto because every element in set Q = {5, 10, 15, 20} does not have a pre-image in set P = {10, 20, 30} (20 does not have a pre-image in set P).
f = {(10, 5), (10, 10), (10, 15), (10, 20)} and f = {(10, 5), (10, 10), (20, 15), (30, 20)} are many – one onto.
f = {(20, 5), (20, 10), (30, 10)} is neither one – one nor onto.
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Community Answer
Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the followi...
Explanation:

One – one Function:
- A function is said to be one – one if each element in the domain is mapped to a unique element in the codomain.
- In other words, no two different elements in the domain can map to the same element in the codomain.

Onto Function:
- A function is said to be onto if each element in the codomain has at least one pre-image in the domain.
- In other words, every element in the codomain is mapped to from at least one element in the domain.

Given Sets:
P = {10, 20, 30} and Q = {5, 10, 15, 20}

Analysis of Options:
- Option 'A': This function is not one – one as 10 is mapped to multiple elements in Q.
- Option 'B': This function is one – one as each element in P is mapped to a unique element in Q. However, it is not onto as elements 5, 15, and 20 in Q do not have pre-images in P.
- Option 'C': This function is not one – one as 20 is mapped to multiple elements in Q.
- Option 'D': This function is not one – one as 10 is mapped to multiple elements in Q.

Conclusion:
- Option 'B' (f = {(10, 5), (20, 10), (30, 15)}) is the only function that is one – one but not onto based on the given sets P and Q.
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Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the following functions is one – one and not onto?a)f = {(10, 5), (10, 10), (10, 15), (10, 20)}b)f = {(10, 5), (20, 10), (30, 15)}c)f = {(20, 5), (20, 10), (30, 10)}d)f = {(10, 5), (10, 10), (20, 15), (30, 20)}Correct answer is option 'B'. Can you explain this answer?
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Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the following functions is one – one and not onto?a)f = {(10, 5), (10, 10), (10, 15), (10, 20)}b)f = {(10, 5), (20, 10), (30, 15)}c)f = {(20, 5), (20, 10), (30, 10)}d)f = {(10, 5), (10, 10), (20, 15), (30, 20)}Correct answer is option 'B'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the following functions is one – one and not onto?a)f = {(10, 5), (10, 10), (10, 15), (10, 20)}b)f = {(10, 5), (20, 10), (30, 15)}c)f = {(20, 5), (20, 10), (30, 10)}d)f = {(10, 5), (10, 10), (20, 15), (30, 20)}Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let P = {10, 20, 30} and Q = {5, 10, 15, 20}. Which one of the following functions is one – one and not onto?a)f = {(10, 5), (10, 10), (10, 15), (10, 20)}b)f = {(10, 5), (20, 10), (30, 15)}c)f = {(20, 5), (20, 10), (30, 10)}d)f = {(10, 5), (10, 10), (20, 15), (30, 20)}Correct answer is option 'B'. Can you explain this answer?.
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