Answer to Question #116521 in Discrete Mathematics for inv

Question

1. Write the multisets of prime factors for the given numbers.
I. 160
II. 120
III. 250
2. Write the multiplicities of each element of multisets in part 2(1-I, ii,iii) separately.
3. Find the cardinalities of each multiset in part 2-1.

Answer 1

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

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

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

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

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

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