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Consider the following statements:
S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite.
S2: There exists two irrational numbers x and y such that (x+y) is rational.
 
Q. Which of the following is true about S1 and S2?
  • a)
    Only S1 is correct
  • b)
    Only S2 is correct
  • c)
    Both S1 and S2 are correct
  • d)
    None of S1 and S2 is correct
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider the following statements:S1: There exists infinite sets A, B,...
S1: A ∩ (B ∪ C) Here S1 is finite where A, B, C are infinite We’ll prove this by taking an example. Let A = {Set of all even numbers} = {2, 4, 6, 8, 10...} Let B = {Set of all odd numbers} = {1, 3, 5, 7...........} Let C = {Set of all prime numbers} = {2, 3, 5, 7, 11, 13......} B U C = {1, 2, 3, 5, 7, 9, 11, 13......} A ∩ (B ∪ C) Will be equals to: {2} which is finite. I.e. using A, B, C as infinite sets the statement S1 is finite. So, statement S1 is correct. S2: There exists two irrational numbers x, y such that (x+y) is rational To prove this statement as correct, we take an example. Let X = 2-Sqrt (3), Y = 2+Sqrt (3) => X, Y are irrational X+Y = 2+Sqrt (3) + 2-Sqrt (3) = 2+2 = 4 So, statement S2 is also correct. Answer is Option C Both Statements S1, S2 are correct.
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Consider the following statements:S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite.S2: There exists two irrational numbers x and y such that (x+y) is rational.Q.Which of the following is true about S1 and S2?a)Only S1 is correctb)Only S2 is correctc)Both S1 and S2 are correctd)None of S1 and S2 is correctCorrect answer is option 'C'. Can you explain this answer?
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Consider the following statements:S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite.S2: There exists two irrational numbers x and y such that (x+y) is rational.Q.Which of the following is true about S1 and S2?a)Only S1 is correctb)Only S2 is correctc)Both S1 and S2 are correctd)None of S1 and S2 is correctCorrect 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 Consider the following statements:S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite.S2: There exists two irrational numbers x and y such that (x+y) is rational.Q.Which of the following is true about S1 and S2?a)Only S1 is correctb)Only S2 is correctc)Both S1 and S2 are correctd)None of S1 and S2 is correctCorrect 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 Consider the following statements:S1: There exists infinite sets A, B, C such that A ∩ (B ∪ C) is finite.S2: There exists two irrational numbers x and y such that (x+y) is rational.Q.Which of the following is true about S1 and S2?a)Only S1 is correctb)Only S2 is correctc)Both S1 and S2 are correctd)None of S1 and S2 is correctCorrect answer is option 'C'. Can you explain this answer?.
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