Answer to Question #102496 in Discrete Mathematics for Roshanthi

Question

Part 2
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

1.

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

$\{2,2,2,2,2,5\}$

ii) $120=2^3\times3^1\times 5^1$

$\{2,2,2,3,5\}$

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

$\{2,5,5,5\}$

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