Transcript Unit 1 - Logic

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A mathematical statement must either be true
or false
The variable of an open sentence is
something that can have multiple choices
(i.e. you can ask: who, what, where, when)
The truth set of a domain must be elements
from the domain
The negation inserts or removes the word
“not”. DO NOT CHANGE ANY OTHER WORDS!
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Conjunctions
◦ Connect statements using “and”
◦ Are only TRUE when BOTH statements are TRUE
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Disjunctions
◦ Connect statements using “or”
◦ Are only FALSE when BOTH statements are FALSE
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Connect statements using “if … then”
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p → q is symbolically
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~ means not
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Are only FALSE when the first statement is
TRUE and the second statement is FALSE
◦ Think of it as you kept your promise, but I broke
mine
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Hidden conditionals are statements that can
be written as an “if … then” because the first
part implies the second part
Biconditionals
◦ Connect statements using “if and only if”
◦ Are true when both statements have the SAME truth
value
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Converse
◦ “CO” = change order
◦ Change the order of the 1st and 2nd statements
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Inverse
◦ “IN” = I Negate
◦ Leave the statements in the original order, but
negate both statements
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Contrapositive
◦ LONG WORD = do everything!
◦ Change the order and negate both statements
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Logically equivalent statements
◦ The original conditional and the contrapositive
always have the same truth values