CSC151.02 2015S, Class 15: Boolean Values and Predicate Procedures

Overview

Preliminaries

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Two primary values: true (#t) and false (#f), along with operations on those values.
Why are we learning these things?
- They will be useful when we write conditionals
- Another way to get the computer to do something
- Computers think in 0's and 1's (only two values), so thinking in a world of two values is helpful

Useful to think about functions from Boolean values to Boolean values
equal? and = both give truth values as output.
- check-equal? and check-=
At the most basic level, and and or are functions that take Boolean input values and give Boolean outputs. not.
How might you explain to someone what and, or, or not means?
- and - if both inputs are true, the output is true
- or - if either input is true, the output is true
- not - if the input is true, the output is false
Using that definition, what is the value of (and #t #f)?
```
          input/a
AND    True    False
```
i n True True False p u False False False t / b
```
          input/a
OR     True    False
```
i n True True True
p u False True False t / b

Create the implies function

              input/a
    =>     True    False
i
n  True    True    False
p
u  False   True    True
t
/
b

List all the cases in which => holdsa

(define => (lambda (a b) (or (and a b) (and (not a) b) (and (not a) (not b)))))

A good strategy: Gives you long answers, but gives you an answer

Simplifying the answer: If b holds, we don't care about a

    (define =>
      (lambda (a b)
        (or b (and (not a) (not b)))))

Another approach: Just eliminate the falses

    (define =>
      (lambda (a b)
        (not (and a (not b)))))

Will we know whnat to do in the other cases?

New Question: How many different Boolean functions are there?