# Exercise 1

## Problem

What does each of the following return? Run the code to check your answer.

if (1 == "1") "coercion  works" else "no coercion "

ifelse(5 > c(1, 10, 2), "hello", "olleh")

## Solution

if (1 == "1") "coercion  works" else "no coercion "
#>  "coercion  works"
ifelse(5 > c(1, 10, 2), "hello", "olleh")
#>  "hello" "olleh" "hello"

# Exercise 2

## Problem

Consider two vectors, x and y, each of length one. Write a set of conditionals that satisfy the following.

• If x is positive and y is negative or y is positive and x is negative, print “knits”.
• If x divided by y is positive, print “stink”.
• Stop execution if x or y are zero.

Test your code with various x and y values. Where did you place the stop execution code?

## Solution

x <- 4
y <- -10

if (x == 0 | y == 0) {
stop("One of x or y is 0!")
} else if (x / y > 0) {
print("stink")
} else {
print("knits")
}
#>  "knits"

# Exercise 3

## Problem

Consider the vector x below.

x <- c(3, 4, 12, 19, 23, 49, 100, 63, 70)

Write R code that prints the perfect squares in x.

## Solution

x <- c(3, 4, 12, 19, 23, 49, 100, 63, 70)

for (i in x) {
if (sqrt(i) %% 1) {
next
}
print(i)
}
#>  4
#>  49
#>  100

# Exercise 4

## Problem

Consider z <- c(-1, .5, 0, .5, 1). Write R code that prints the smallest non-negative integer $$k$$ satisfying the inequality $\lvert cos(k) - z \rvert < 0.001$ for each component of z.

## Solution

for (z in c(-1, .5, 0, .5, 1)) {
k <- 0
while (abs(cos(k) - z) >= .001) {
k <- k + 1
}
print(k)
}
#>  22
#>  21766
#>  40459
#>  21766
#>  0