Choose the correct answers from the given four option: Two finite sets have m and n elements. The number of…

Choose the correct answers from the given four option:

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively,

  1. 4, 4

  2. 7, 4

  3. 7, 7

  4. 4, 7

Solution

Solution:

According to the question,

? 2m - 2n = 12

? 2n(2m-n - 1) 24. 7

? 2n = 24 and 2m-n - 1 = 7

? n = 2 and 2m-n = 8

? 2m-n = 23 ? m - n = 3 ? m - 4 = 3 ? m = 7

Asked in: NCERTEXAMPLER

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