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.

2. Function converts Fahrenheit temperatures into Celsius. What is the function for opposite conversion?

Answer 1

1.

$160 : \{2,2,2,2,2,5\}$

multiplicity of 2 is 5, multiplicity of 5 is 1

Cardinality$=6$

$120 : \{2,2,2,3,5\}$

multiplicity of 2 is 3, multiplicity of 3 is 1, multiplicity of 5 is 1

Cardinality$=5$

$250 : \{2,5,5,5\}$

multiplicity of 2 is 1, multiplicity of 5 is 3

Cardinality$=4$

2.

Function converts Fahrenheit temperatures into Celsius:

$T_{\degree C}=\frac {5}{9}(T_{(\degree F)}-32)$

Then:

$T_{(\degree F)}-32=\frac {9}{5}T_{(\degree C)}$

The function for opposite conversion:

$T_{(\degree F)}=\frac {9}{5}T_{(\degree C)}+32$