Lecture 4: Truth
functions, evaluating
compound statements
1. Functions, arithmetic functions, and
truth functions
2. Definitions of truth functions
3. Evaluating compound expressions
4. Categorizing statements
Functions
A function is something that takes inputs
and produces outputs.
You can think of them as a sort of
abstract
machine  like a bread machine
that will produce as ‘output’ bread, if it
is given as ‘input’ flour, yeast, sugar, etc.
Arithmetic Functions
Familiar examples of functions are the
arithmetic
functions addition,
subtraction, multiplication and division
Addition takes 2 numbers as input, and
produces 1 number as output
If you input 4 and 3, it outputs 7
Addition takes 2 numbers as input, and
produces 1 number as output
If you input 4 and 3, it outputs 7
A function can be defined in terms of its
entire inputoutput structure
x
y
x+y
1
1
2
1
2
3
2
1
3
2
2
4
A function can be defined in terms of its
entire inputoutput structure
x
y
x+y
1
1
2
1
2
3
2
1
3
2
2
4
x
y
x
㱸
y
1
1
2
1
2
3
2
1
3
2
2
4
Addition ‘+’
Rickification ‘
㱸
’
x
y
x+y
1
1
2
1
2
3
2
1
3
2
2
4
Addition ‘+’
x
y
x
x
y
1
1
1
1
2
2
2
1
2
2
2
4
Multiplication ‘x’
x
y
xy
1
1
0
1
2
1
2
1
1
2
2
0
Subtraction ‘’
x
y
x
÷
y
1
1
1
1
2
.5
2
1
2
2
2
1
Division ‘+’
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Truth Functions
Truth functions are functions that take
truth values as inputs, and produce truth
values as outputs.
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 Spring '08
 churchland
 Logic, Addition, Logical connective, Shelly

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