Question #284658

1.     Write the multisets (bags) of prime factors of given numbers.

i.       160

ii.      120

iii.    250

2.     Write the multiplicities of each element of multisets (bags) in Part 2-1(i,ii,iii) separately.

3.     Determine the cardinalities of each multiset (bag) in Part 2-1(i,ii,iii).


1
Expert's answer
2022-01-04T17:54:14-0500

Solution:

i)160=25×51i) 160=2^5\times 5^1

ii)120=23×31×51ii) 120=2^3 \times 3^1\times 5^1

iii)250=21×53iii) 250=2^1\times5^3


1) So, Multiset of 160 of prime factors = {2,2,2,2,2,5}\{2, 2,2,2,2,5\}

Multiset of 120 of prime factors = {2,2,2,3,5}\{2, 2,2,3, 5\}

Multiset of 250 of prime factors = {2,5,5,5}\{2, 5,5,5\}


2)

i) 2 has multiplicity 5,

5 has multiplicity 1

ii) 2 has multiplicity 3,

3 has multiplicity 1,

5 has multiplicity 1

iii) 2 has multiplicity 1

5 has multiplicity 3


3) i)A={2,2,2,2,2,5},    A=6i) A=\{2,2,2,2,2,5\}, \;\; |A|=6

ii)A={2,2,2,3,5},    A=5ii) A=\{2,2,2,3,5\},\;\; |A|=5

iii)A={2,5,5,5},    A=4iii) A=\{2,5,5,5\},\;\; |A|=4

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