Answer to Question #284658 in Discrete Mathematics for darshi

Question

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).

Answer 1

Solution:

$i) 160=2^5\times 5^1$

$ii) 120=2^3 \times 3^1\times 5^1$

$iii) 250=2^1\times5^3$

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

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

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

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) $i) A=\{2,2,2,2,2,5\}, \;\; |A|=6$

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

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