Show by using "proof by contradiction" that the set of binary sequences {0,1}n is uncountable.

You can prove this important result as follows:

Step-by-step explanation:

Let be the set of all binary sequences, that is to say, . Suppose that is a countable set. Then the elements of   can be ordered as a sequence , where each is a binary sequence. The digit of each sequence is expressed by . Define the sequence as follows:

Note that differ from each in at least one digit. Then for all , then . This contradicts the fact that is the set of all binary sequences. Then must be a uncountable set.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

50.6

step-by-step explanation: