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19 Cards in this Set
- Front
- Back
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A conditional/implicative statement is... |
an if-then statement. |
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Antecedent/Hypothesis |
the part p following if. |
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Consequent/Conclusion |
the part q following then |
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How is the following statement read? p》q |
Read as: •“if p then q” • “p implies q.”
When determing the truth of the statement it is read as •"If P is true than Q is true" |
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Converse |
Written as: q》p
Ex: If the grass is wet then it is raining |
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Inverse |
Written as: ~p》~q
Ex: If it is not raining than the grass is not wet |
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Contrapositive |
Written as: ~q》~p
If the field is not wet than it is not raining |
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Conditional |
Written as: p》q
Ex: If it is raining then the grass is wet |
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The negation of a statement p is the... |
opposite of the statement. The symbol is ~p and is read “not p.”
Ex: The negation of the statement “The sky is blue” is “The sky is not blue.” |
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Determing the Truth of a Conditional Statement |
It is true... •If the antecedent is true and the consequent is true •If the antecedent is false
It is false... •If the antecedent is true and the consequent is false
P》Q can be read an the rule "If p is true than q is true" (If p is true than q must also be true for the statement to be true) Using that rule one can determine if a statement is true or not when utilizing a truth table
If p is not true than the initial assumption the statement is based on does not apply (is not applicable) As a result you would label the statement as true as there is no way of determining the truth of the statement
The statement relies on the initial statement to prove the conditional statement true or false Since the initial statement does not apply there is no way of determining the truth and no way of proving it false so it is labeled as true |
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Determing the Truth of Biconditional Statement |
A Bi-conditional statement is true... •If the antecedent and consequent and both true •If the antecedent and consequent and both false (If p and q are either both true or both false)
(True if both are the same)
A Bi-conditional Statement is false... •If the antecedent is true and the consequent is false •If the antecedent is false and the consequent is true (If p and q are opposite)
Ex: P《-》Q |
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Disjunction Statement |
-An "or" statement -Denoted by v -True when the antecedent and consequent are both not false -Only false when both the antecedent and consequent are false |
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Conjunction Statement |
-An "and" statement -Denoted by ^ -Only true when both statements are true |
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Biconditional Statement |
A biconditional is a single true statement that combines a true conditional and its true converse. You can write a biconditional by joining the two parts of each conditional with the phrase if and only if.
-Denoted by a double sided arrow Ex: P《-》Q |
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Truth Values of P on a Truth Table |
T T F F |
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Truth Values of Q on a Truth Table |
T F T F |
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Truth Values of ~P on a Truth Table |
F F T T |
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Truth Values of ~Q on a Truth Table |
F T F T |
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Types of Conditional Statements |
Conditional Converse Inverse Contrapositive |
