Logische Operatoren und boolesche Logik

Einführung in die boolesche Logik

# Boolean values in R
is_raining <- TRUE
is_cold <- FALSE
cat('Is raining:', is_raining, '
')
cat('Is cold:', is_cold, '
')
cat('Class:', class(is_raining), '
')

Elementweises AND mit &

ages <- c(15, 22, 17, 30, 19)
has_id <- c(FALSE, TRUE, FALSE, TRUE, TRUE)

# Can buy alcohol? (must be 18+ AND have ID)
can_buy <- (ages >= 18) & has_id
cat('Ages >= 18:', ages >= 18, '
')
cat('Has ID:', has_id, '
')
cat('Can buy:', can_buy, '
')

Elementweises OR mit |

scores_math <- c(85, 45, 72, 38, 90)
scores_english <- c(40, 88, 65, 70, 55)

# Pass if either subject >= 60
passes <- (scores_math >= 60) | (scores_english >= 60)
cat('Math pass:', scores_math >= 60, '
')
cat('English pass:', scores_english >= 60, '
')
cat('Overall pass:', passes, '
')

Logisches NOT mit !

is_weekend <- c(TRUE, FALSE, FALSE, FALSE, FALSE, TRUE, TRUE)
cat('Is weekend:', is_weekend, '
')
cat('Is weekday:', !is_weekend, '
')

# Count weekdays
cat('Number of weekdays:', sum(!is_weekend), '
')

Skalares AND mit &&

x <- 10

# Short-circuit: second condition skipped if first is FALSE
if (x > 0 && x < 100) {
  cat('x is a positive double-digit or less
')
}

# && only looks at first element
cat('TRUE && FALSE:', TRUE && FALSE, '
')
cat('TRUE & FALSE (vectorised):', TRUE & FALSE, '
')

Skalares OR mit ||

user_role <- 'admin'

# Short-circuit OR — stops at first TRUE
if (user_role == 'admin' || user_role == 'superuser') {
  cat('Access granted
')
} else {
  cat('Access denied
')
}

cat('FALSE || TRUE:', FALSE || TRUE, '
')

Exklusives OR mit xor()

# xor truth table
cat('xor(TRUE, TRUE):', xor(TRUE, TRUE), '
')   # FALSE
cat('xor(TRUE, FALSE):', xor(TRUE, FALSE), '
')  # TRUE
cat('xor(FALSE, TRUE):', xor(FALSE, TRUE), '
')  # TRUE
cat('xor(FALSE, FALSE):', xor(FALSE, FALSE), '
') # FALSE

# Practical: exactly one sensor triggered
sensor_a <- c(TRUE, FALSE, TRUE, FALSE)
sensor_b <- c(FALSE, FALSE, TRUE, TRUE)
cat('Exactly one sensor:', xor(sensor_a, sensor_b), '
')

any() und all()

temperatures <- c(22.1, 24.5, 19.8, 31.2, 28.0)

cat('Any temperature above 30?', any(temperatures > 30), '
')
cat('All temperatures above 15?', all(temperatures > 15), '
')
cat('All temperatures above 25?', all(temperatures > 25), '
')

# Useful for data validation
test_scores <- c(78, 85, 92, 88, 76)
cat('All passed (>=60)?', all(test_scores >= 60), '
')

Logische Operatoren kombinieren

age <- 25
income <- 55000
credit_score <- 720

# Loan eligibility: age 21-65, income >= 40000, credit >= 700
eligible <- (age >= 21 && age <= 65) &&
            (income >= 40000) &&
            (credit_score >= 700)
cat('Loan eligible:', eligible, '
')

Logische Operatoren auf Data Frames

# Simple data frame
names_vec <- c('Alice', 'Bob', 'Carol', 'Dave', 'Eve')
ages_vec <- c(28, 35, 22, 45, 31)
salaries <- c(55000, 72000, 38000, 90000, 61000)

# Filter: age 25-40 AND salary above 50000
mask <- (ages_vec >= 25 & ages_vec <= 40) & (salaries > 50000)
cat('Matching employees:', names_vec[mask], '
')

Boolesche Arithmetik

responses <- c(TRUE, FALSE, TRUE, TRUE, FALSE, TRUE, FALSE, TRUE)

cat('Number of TRUE:', sum(responses), '
')
cat('Proportion TRUE:', mean(responses), '
')
cat('Percentage:', mean(responses) * 100, '%
')

# Count values meeting a condition
scores <- c(88, 45, 92, 61, 73, 55, 84)
cat('Number passing (>=60):', sum(scores >= 60), '
')

Kurzer Test

Wiederholung: Boolesche Logik in R

# Summary: all logical operators at a glance
x <- c(TRUE, FALSE, TRUE)
y <- c(TRUE, TRUE, FALSE)
cat('x & y :', x & y, '
')
cat('x | y :', x | y, '
')
cat('!x    :', !x, '
')
cat('xor   :', xor(x, y), '
')
cat('any(x):', any(x), '
')
cat('all(x):', all(x), '
')