Set, Relations and FunctionsPYQ June 19Question 1888 of 217
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The no. of subsets of the set (3,4,5)\displaystyle (3, 4, 5) is:

Options

A4
B8
C16
D32
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Correct Answer

✅ Option b — 8

All Options:

  • A4
  • B8
  • C16
  • D32

Detailed Solution & Explanation

The given set is S={3,4,5}\displaystyle S = \{3, 4, 5\}.
Let n\displaystyle n represent the number of elements in the set S\displaystyle S. Here, n=3\displaystyle n = 3.
The formula for the total number of subsets of a set with n\displaystyle n elements is:
Number of Subsets=2n\text{Number of Subsets} = 2^n
Substituting n=3\displaystyle n = 3:
Number of Subsets=23=8\text{Number of Subsets} = 2^3 = 8
The 8\displaystyle 8 subsets are explicitly:
∅,{3},{4},{5},{3,4},{3,5},{4,5},{3,4,5}\emptyset, \{3\}, \{4\}, \{5\}, \{3, 4\}, \{3, 5\}, \{4, 5\}, \{3, 4, 5\}
Hence, **Option B** is the correct answer.

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