Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Let f be a function from a set A to a set B, ...
Start Learning for Free
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a ∈ A. Which of the following statements is always true for all such functions f and g?
- a)g is onto => h is onto
- b)h is onto => f is onto
- c)h is onto => g is onto
- d)h is onto => f and g are ont
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Let f be a function from a set A to a set B, g a function from B to C,...
Explanation:
To prove that the statement "h is onto = g is onto" is always true for all functions f and g, we need to show that if h is onto, then g is onto, and vice versa.
Proof:
1. Suppose h is onto. This means that for every element c in set C, there exists an element a in set A such that h(a) = c.
2. Let's consider an arbitrary element c in set C. Since h is onto, there exists an element a in set A such that h(a) = c.
3. According to the definition of h, we have h(a) = g(f(a)). So, c = g(f(a)).
4. This implies that for every element c in set C, there exists an element b = f(a) in set B such that g(b) = c.
5. Therefore, g is onto.
Proof (continued):
1. Suppose g is onto. This means that for every element c in set C, there exists an element b in set B such that g(b) = c.
2. Let's consider an arbitrary element c in set C. Since g is onto, there exists an element b in set B such that g(b) = c.
3. According to the definition of g, there exists an element a = f^(-1)(b) in set A such that f(a) = b.
4. This implies that for every element c in set C, there exists an element a = f^(-1)(b) in set A such that h(a) = g(f(a)) = g(b) = c.
5. Therefore, h is onto.
Conclusion:
From the two proofs above, we can conclude that if h is onto, then g is onto, and vice versa. Therefore, the statement "h is onto = g is onto" is always true for all functions f and g.
To prove that the statement "h is onto = g is onto" is always true for all functions f and g, we need to show that if h is onto, then g is onto, and vice versa.
Proof:
1. Suppose h is onto. This means that for every element c in set C, there exists an element a in set A such that h(a) = c.
2. Let's consider an arbitrary element c in set C. Since h is onto, there exists an element a in set A such that h(a) = c.
3. According to the definition of h, we have h(a) = g(f(a)). So, c = g(f(a)).
4. This implies that for every element c in set C, there exists an element b = f(a) in set B such that g(b) = c.
5. Therefore, g is onto.
Proof (continued):
1. Suppose g is onto. This means that for every element c in set C, there exists an element b in set B such that g(b) = c.
2. Let's consider an arbitrary element c in set C. Since g is onto, there exists an element b in set B such that g(b) = c.
3. According to the definition of g, there exists an element a = f^(-1)(b) in set A such that f(a) = b.
4. This implies that for every element c in set C, there exists an element a = f^(-1)(b) in set A such that h(a) = g(f(a)) = g(b) = c.
5. Therefore, h is onto.
Conclusion:
From the two proofs above, we can conclude that if h is onto, then g is onto, and vice versa. Therefore, the statement "h is onto = g is onto" is always true for all functions f and g.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer?
Question Description
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer?.
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let f be a function from a set A to a set B, g a function from B to C, and h a function from A to C, such that h(a) = g(f(a)) for all a A. Which of the following statements is always true for all such functions f and g? a)g is onto = h is ontob)h is onto = f is ontoc)h is onto = g is ontod)h is onto = f and g are ontCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup