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If sd V = 1, 2, 3, how many subsets does it have? 10) Find the HCF of 19 and 127.

Mathematics

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Part 9· 3 steps

If set V={1,2,3}V = \{1, 2, 3\}, how many subsets does it have?

  1. Determine the number of elements in the set VV.

    The set V={1,2,3}V = \{1, 2, 3\} has n=3n = 3 elements.

  2. Use the formula for the number of subsets.

    The number of subsets of a set with nn elements is given by 2n2^n.

  3. Calculate the number of subsets.

    Number of subsets=23=2×2×2=8\text{Number of subsets} = 2^3 = 2 \times 2 \times 2 = 8

    The set VV has 8\boxed{8} subsets.

Part 111

Find the HCF of 119 and 127.

  1. Find the prime factorization of 119.

    119=7×17119 = 7 \times 17
  2. Find the prime factorization of 127.

    127 is a prime number, so its only prime factor is itself.

    127=127127 = 127
  3. Identify the common prime factors.

    The prime factors of 119 are 7 and 17.
    The prime factor of 127 is 127.
    There are no common prime factors other than 1.

  4. Determine the HCF.

    When two numbers have no common prime factors other than 1, their Highest Common Factor (HCF) is 1.

    HCF(119,127)=1\text{HCF}(119, 127) = 1

    The HCF of 119 and 127 is 1\boxed{1}.

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