NDA 2019 Maths · Mathematics · Sets, Relations and Functions · medium

The number of subsets of \1,2,3,4,5,6\ that contain the element 1 but do not contain the element 6 is

Single correct option

The number of subsets of

\{1,2,3,4,5,6\}

that contain the element

1

but do not contain the element

6

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Answer: (A) $16$

Fix the two special elements:

1

must be present and

6

must be absent, so only the remaining four elements

2,3,4,5

are free. Each of them can either be included or left out, giving

2^4=16

subsets. The answer

32

counts subsets containing

1

with no condition on

6

, and

8

wrongly fixes one more element.

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