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Questions and Answers
What is the definition of a conditional statement?
What is the definition of a conditional statement?
- q to p
- -p to -q
- p to q (correct)
- -q to -p
What is the definition of inverse?
What is the definition of inverse?
-p to -q
What is the definition of converse?
What is the definition of converse?
q to p
What is the definition of contrapositive?
What is the definition of contrapositive?
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What does the law of detachment state?
What does the law of detachment state?
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What does the law of syllogism state?
What does the law of syllogism state?
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What is the definition of a biconditional statement?
What is the definition of a biconditional statement?
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Study Notes
Conditional Statements and Their Variations
- A conditional statement has the form "if p, then q" represented as p to q.
- The inverse of a conditional statement negates both the hypothesis and conclusion, represented as -p to -q.
- The converse flips the hypothesis and conclusion; it is written as q to p.
- The contrapositive involves negating both parts of the converse, represented as -q to -p.
Principles of Logical Reasoning
- The law of detachment states that if a conditional statement p to q is true and p is true, then q must also be true.
- The law of syllogism allows for deriving a new conditional statement; if p to q is true and q to r is true, then it follows that p to r is true.
Biconditional Statements
- A biconditional statement indicates that p is true if and only if q is true, represented as p (---) q.
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