$1.$ Introduction to R Using Boolean Logic

Write a piece of R code that you could use to teach a seven$-$year$-$old child about Boolean logic. If you have never encountered Boolean logic before $($sometimes it is called Boolean algebra$),$ you will have to look it up to discover the three essential operations $($AND$,$ OR$,$ NOT$)$ and how they work. In addition, you will have to discover the $$operators$($i$.$e$.,$ the special punctuation marks$)$ that R uses to represent Boolean operations.

For example, here is a single line of code $($and the response from the R$-$console in bold$)$ that represents one of the two possible outcomes of the AND operator:

$>$ # This line shows the Boolean AND function at work

$>1$ & $1$

$[1]$ TRUE

Take note of several important aspects of this example: $(1)$ It has a comment that explains a little bit of what is going on $($all of the stuff after the # character$).(2)$ It needs more comments if it is going to be helpful to a seven$-$year$-$old. $(3)$ More lines of code are needed to demonstrate the other outcome of AND, as well as all of the outcomes of OR and NOT. Keeping your seven$-$year$-$old in mind, write and submit the rest of the code and comments.

Then use these conditional statements within a if statement to printout the expected logic. For example:

$>$ # show the use of an $$if$$ statement $-$ that $1$&$1$ is true

$>$ if$(1$&$1)$ print$(1$&$1$ is true$)$ else print$($error somewhere$)$

Three logical operators:

& $($And$)$: if A and B are TRUE then and then only it is TRUE or $1,$ otherwise always FALSE

I $($Or$)$: if either A and B both are FALSE then it's FALSE otherwise it is always TRUE

$!($Not$)$: Basically flips the TRUE to FALSE, vice versa

$2.$ Vectors

Define the following vectors, which represent the weight and height of people on a particular team $($in inches and pounds$)$:

height $<-$ c$(59,60,61,58,67,72,70)$

weight $<-$ c$(150,140,180,220,160,140,130)$

Define a variable:

a $<-150$

Now that you have some data $$ explore!

Step $1$: Calculating means

Compute, using R$,$ the average height $($called mean in R$).$

Compute, using R$,$ the average weight $($called mean in R$).$

Calculate the length of the vector $$height$$ and $$weight$.$

Calculate the sum of the heights.

Compute the average of both height and weight, by dividing the sum $($of the height or the width, as appropriate$),$ by the length of the vector. How does this compare to the $$mean$$ function?

Step $2$: Using max$/$min functions

Compute the max height, store the result in $$maxH$.$

Compute the min weight, store the results in $$minW$.$

Step $3$: Vector math

Create a new vector, which is the weight $+5($every person gained $5$ pounds$).$

Compute the weight$/$height $($weight divided by height$)$ for each person, using the new weight just created.

Step $4$: Using conditional if statements

$***$ The syntax for if else statement is: if $($test$\_$expression$)\{$statement$1\}$ else $\{$statement$2\}$

Hint: In R$,$ one can do:

if $(100<150)100$ is less than $150$ else $100$ is greater than $150$

Write the R code to test if max height is greater than $60($output $$yes$$ or $$no$).$

Write the R code to test if min weight is greater than the variable $$a$($output $$yes$$ or $$no$).$