Answer to Question #120781 in Discrete Mathematics for Roshanthi

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:

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