Set, Relations and FunctionsPYQ June 19Question 1887 of 217
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If A=(1,2,3,4,5,6,7,8,9)\displaystyle A = (1, 2, 3, 4, 5, 6, 7, 8, 9) B=(1,3,4,5,7,8)\displaystyle B = (1, 3, 4, 5, 7, 8) C=(2,6,8)\displaystyle C = (2, 6, 8) then find (A−B)∪C\displaystyle (A - B) \cup C

Options

A(2,6,8)\displaystyle (2, 6, 8)
B(2,6,8)\displaystyle (2, 6, 8)
C(2,6,8,9)\displaystyle (2, 6, 8, 9)
DNone of these
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Correct Answer

✅ Option c — (2,6,8,9)\displaystyle (2, 6, 8, 9)

All Options:

  • A(2,6,8)\displaystyle (2, 6, 8)
  • B(2,6,8)\displaystyle (2, 6, 8)
  • C(2,6,8,9)\displaystyle (2, 6, 8, 9)
  • DNone of these

Detailed Solution & Explanation

Given sets:
A={1,2,3,4,5,6,7,8,9}\displaystyle A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}
B={1,3,4,5,7,8}\displaystyle B = \{1, 3, 4, 5, 7, 8\}
C={2,6,8}\displaystyle C = \{2, 6, 8\}
First, let us find the difference set A−B\displaystyle A - B, which contains elements in A\displaystyle A but not in B\displaystyle B:
A−B={2,6,9}A - B = \{2, 6, 9\}
Now, we compute the union of (A−B)\displaystyle (A - B) with C\displaystyle C:
(A−B)∪C={2,6,9}∪{2,6,8}(A - B) \cup C = \{2, 6, 9\} \cup \{2, 6, 8\}
The union of two sets is the set of all elements that are in either set:
(A−B)∪C={2,6,8,9}(A - B) \cup C = \{2, 6, 8, 9\}
Hence, **Option C** is the correct answer.

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