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GMAT Exam  >  GMAT Questions  >  There exists a setX= {1, 2, 3, 4}. Which of t... Start Learning for Free
There exists a set X = {1, 2, 3, 4}.  Which of the following defines a function of X?
  • a)
    h={(2,1),(3,4),(1,4),(2,1),(4,4)}
  • b)
    two are functions
  • c)
    g={(3,1),(4,2),(1,1)}
  • d)
    f={(2,3),(1,4),(2,1),(3,2),(4,4)}
  • e)
    none are functions
Correct answer is option 'A'. Can you explain this answer?
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There exists a setX= {1, 2, 3, 4}. Which of the following defines a fu...
Let's look at f,g,and h and see if any of them are functions.
1. f = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of X because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. g = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of X because it contains no ordered pair with first coordinate 2.  Because the set X = {1, 2, 3, 4}, we need an ordered pair of the form (2,  ) .
3. h = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function.  Even though two of the ordered pairs have the same number (2) as the first coordinate, h is still a function of X because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
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There exists a setX= {1, 2, 3, 4}. Which of the following defines a fu...
Answer:

Introduction:
In order for a set to define a function, each input (or element) in the set must have a unique output. In other words, no two elements in the set can have the same output.

Explanation:
Let's analyze each option to see if it defines a function of X.

Option A:
h={(2,1),(3,4),(1,4),(2,1),(4,4)}
- This option defines a function because every input in set X has a unique output. For example, 2 maps to 1, 3 maps to 4, 1 maps to 4, and 4 maps to 4.

Option B:
two are functions
- This option does not provide any information about the functions. It is not a valid answer.

Option C:
g={(3,1),(4,2),(1,1)}
- This option also defines a function because each input in set X has a unique output. For example, 3 maps to 1, 4 maps to 2, and 1 maps to 1.

Option D:
f={(2,3),(1,4),(2,1),(3,2),(4,4)}
- This option does not define a function because the input 2 has two different outputs, 3 and 1. Therefore, it violates the rule that each input must have a unique output.

Option E:
none are functions
- This option is not a valid answer as it does not provide any information about the functions.

Conclusion:
Based on the analysis, only option A, h={(2,1),(3,4),(1,4),(2,1),(4,4)}, defines a function of set X. It is the correct answer.
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In recent years, a class of drugs known as COX-2 inhibitors has gotten much publicity for the drugs’ power to relieve inflammation and pain. These drugs are relatively new to the pharmaceutical industry, their mechanisms of action having been discovered only in 1971. That year, John Vane discovered the relationship between nonsteroidal antiinflammatory drugs, such as aspirin, and a group of molecules, called prostaglandins, responsible for producing the sensation of pain in the human body, among other functions.Prostaglandins were first discovered in the 1930s and are now known to be generated by most mammalian tissues in response to external stimuli. Unlike classical hormones that are synthesized in one tissue but act on a distant one, prostaglandins act on the cells that produce them or on cells located close to the prostaglandins’ cells of origin.Aspirin alleviates pain by inhibiting the function of an enzyme called cyclooxygenase or COX; this inhibition prevents the production of prostaglandins. The three forms of this enzyme, COX-1, COX-2, and COX-3, all stimulate the production of prostaglandins, but each serves a different purpose. COX-1 functions to protect the stomach from irritating gastric acids. COX-2 functions to induce inflammation in injured tissue and COX-3 functions to control the sensation of pain. Aspirin and other similar drugs, such as naproxen, inhibit both COX-1 and COX-2, sometimes producing or aggravating stomach ulcers in patients who take them.In order to eliminate the side effects of aspirin and related drugs, several pharmaceutical companies in the 1990s developed drugs that inhibited only COX-2. However, side effects almost always cropped up, even after clinical trials that seemed to indicate none. This often occurs because trials are conducted within very limited parameters; once the drug has been approved for mass distribution, however, the number of people taking it and the length of time that it is taken increase dramatically. Several COX-2 drugs that have been popular in recent years fit this pattern: initially successful in clinical trials, subsequent studies showed them to have serious, potentially lethal side effects.Though prostaglandin chemistry and enzymology have been studied for half a century, pinpointing the exact role of the molecules in physiological processes still remains a challenge for researchers. Hence it is not surprising that recent therapeutic attempts to interfere with the formation of certain prostaglandins have produced unexpected side effects. It now seems that the hype surrounding COX-2 drugs may have been premature.Q. The passage suggest which the following about COX2 inhibitors?

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There exists a setX= {1, 2, 3, 4}. Which of the following defines a function ofX?a)h={(2,1),(3,4),(1,4),(2,1),(4,4)}b)two are functionsc)g={(3,1),(4,2),(1,1)}d)f={(2,3),(1,4),(2,1),(3,2),(4,4)}e)none are functionsCorrect answer is option 'A'. Can you explain this answer?
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There exists a setX= {1, 2, 3, 4}. Which of the following defines a function ofX?a)h={(2,1),(3,4),(1,4),(2,1),(4,4)}b)two are functionsc)g={(3,1),(4,2),(1,1)}d)f={(2,3),(1,4),(2,1),(3,2),(4,4)}e)none are functionsCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about There exists a setX= {1, 2, 3, 4}. Which of the following defines a function ofX?a)h={(2,1),(3,4),(1,4),(2,1),(4,4)}b)two are functionsc)g={(3,1),(4,2),(1,1)}d)f={(2,3),(1,4),(2,1),(3,2),(4,4)}e)none are functionsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There exists a setX= {1, 2, 3, 4}. Which of the following defines a function ofX?a)h={(2,1),(3,4),(1,4),(2,1),(4,4)}b)two are functionsc)g={(3,1),(4,2),(1,1)}d)f={(2,3),(1,4),(2,1),(3,2),(4,4)}e)none are functionsCorrect answer is option 'A'. Can you explain this answer?.
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