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If A = {x : x is a multiple of 7},
B = {x : x is a multiple of 5} and
C = {x : x is a multiple of 35}
Q. Then which of the following is null set?
  • a)
    (A – B) ∪ C
  • b)
    (A – B) – C 
  • c)
    (A ∩ B) ∩ C
  • d)
    (A ∩ B) – C 
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If A = {x : x is a multiple of 7},B = {x : x is a multiple of 5} andC ...
A = {x : x is a multiple of 7} = {7, 14, 21, 28, 35………..}
B = {x : x is a multiple of 5} = {5, 10, 15, 20, 25………..}
C = {x : x is a multiple of 35} = {35, 70, 105, 140……..}
Checking all the options:
(A – B) ∪ C = {7, 14, 21, 28, 42 …..} ∪ {35, 70, 105, 140……..} = {7, 14, 21, 28, 35, 42, 49…}
Hence it is not a null set.
(A – B) – C = {7, 14, 21, 28, 42 …..} – {35, 70, 105, 140……..} = {7, 14, 21, 28, 42, 49….}
Hence it is not a null set.
(A ∩ B) ∩ C = {35, 70, 105, 140……} ∩ {35, 70, 105, 140……..} = {35, 70, 105, 140……..}
Hence it is not a null set.
(A ∩ B) – C = {35, 70, 105, 140……} – {35, 70, 105, 140……..} = ∅
Hence it is a null set.
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If A = {x : x is a multiple of 7},B = {x : x is a multiple of 5} andC = {x : x is a multiple of 35}Q. Then which of the following is null set?a)(A – B) ∪ Cb)(A – B) – Cc)(A ∩ B) ∩ Cd)(A ∩ B) – CCorrect answer is option 'D'. Can you explain this answer? for Defence 2025 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If A = {x : x is a multiple of 7},B = {x : x is a multiple of 5} andC = {x : x is a multiple of 35}Q. Then which of the following is null set?a)(A – B) ∪ Cb)(A – B) – Cc)(A ∩ B) ∩ Cd)(A ∩ B) – CCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = {x : x is a multiple of 7},B = {x : x is a multiple of 5} andC = {x : x is a multiple of 35}Q. Then which of the following is null set?a)(A – B) ∪ Cb)(A – B) – Cc)(A ∩ B) ∩ Cd)(A ∩ B) – CCorrect answer is option 'D'. Can you explain this answer?.
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