(S7: A set of passwords with a size of 2.9714*10^23.)

Q1. Consider a hashing function H2. It’s domain is S7, and it’s range is N(6) (six digit numbers). What is the cardinality of the range of H2?

Q2. Consider the following statement. “If a function’s range is smaller than its domain, then that function cannot be injective”

Prove or refute this statement.
Based on your proof, what is the implication for H2?
Could there be a function D1 that is the inverse of H2?
What is the implication for using H2 to hide passwords? What might happen if hashed passwords leaked?

Answer:

Step-by-step explanation:

The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.

As the range is a 6 digit number. Each digit can be 0,1,2,...9 (total 10 choices).

Possible numbers in range are 10^6

Therefore the cardinality of the range is 10^6.

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The total nom of  code that can be used is equal to 5+3 = 8

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The answer is in the image 

The solution is given in the image below

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.