If p has 63 subsets find number of p

Mathematics

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Answer

6\text{6}

Step-by-step solution

4 steps

Ili kutatua swali hili, tutachukulia kuwa "subsets" inarejelea proper subsets kwa sababu 63 si namba inayoweza kuwakilishwa kama 2n2^n ambapo nn ni integer (idadi ya elements). Idadi ya proper subsets ya seti yenye nn elements ni 2n−12^n - 1.

  1. Andika formula ya idadi ya proper subsets.

    Ikiwa seti pp ina nn elements, basi idadi ya proper subsets ni 2n−12^n - 1.

  2. Weka idadi ya proper subsets sawa na 63.

    2n−1=632^n - 1 = 63

  3. Tatua mlinganyo ili kupata nn.

    Ongeza 1 pande zote mbili za mlinganyo:

    2n=63+12^n = 63 + 1 2n=642^n = 64

  4. Tafuta thamani ya nn kwa kuandika 64 kama nguvu ya 2.

    Tunajua kuwa 26=642^6 = 64.
    Hivyo,

    2n=262^n = 2^6 n=6n = 6

    Idadi ya elements katika seti pp ni 6.

    Jibu: 6\text{6}

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