Section 2.1 Exercises Solutions | Desklib

Assignment 3.1 - Section 2.1 Exercises
1.
a.
#1 if there is no sufficient water, there is no healthy plant growth
#2 sufficient water follows from healthy plant growth
b.
#1 if there is no further technological advances, there is no increased availability of information
#2 if there is technological advances, there is increased availability of information
c.
#1 if there was no modification of the program, errors were not introduced
#2 is there was modification of the program, errors were introduced
d.
#1 if there is no storm windows or good insulation, there is no fuel saving
#2 if there is no insulation or storm windows throughout, there is no fuel saving
4.
a.
Taking a as 2 and b as 3
2 0 3=0 and 3 0 2=0- in this case a is not equal to b
Hence, the statement does not stand in this case
b.
-12 > 0 yet -1 is less than 0
c.
82 +1 = 65
65 is divisible by 13 and 5
d.
7 is a positive integer
73= 343
But
7!= 5040

Therefore, n3 < n!.
6.
In this case, all the numbers are has to be even such that 3n+2 = even number.
8.
a.
If even number y is 2 then the odd x number is
2+7=9
Where now
X-y = 7
9-2= 7
b
Let x be odd and y be even. Then x = 2m + 1, y = 2m, where m is an integer, and x − y =
2m + 1 − 2m = 1.
There is the assumption that the two numbers are consecutive which is not always the case
10.
Even numbers between 4 ≤ n ≤ 12 are
4,6, 8,10,12
Even integers are given by 2n where n=2,3,4......n
First value 4
4= 3+1 where 3 and 1 are prime numbers
The second number
6= 3+3 or
= 5+1 where 1,3 and 5 are prime numbers
Therefore, from the two numbers test done above, the even numbers are the sum of prime
numbers.
12.
In this case lower limit = 2 and the upper limit = 4
2n= 4
N2= 4
Therefore, it is true to say
For 2 ≤ n ≤ 4, n2 ≥ 2n.