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Propositional Logic - Coggle Diagram
Propositional Logic
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Logical Equivalences
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De Morgan’s Laws
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"Not (p and q) is equivalent to (not p) or (not q)."
"Not (p or q) is equivalent to (not p) and (not q)."
Distributive Laws
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"p and (q or r) is equivalent to (p and q) or (p and r)."
"p or (q and r) is equivalent to (p or q) and (p or r)."
Logical Implications
Definition: An implication p → q means if p is true, then q must be true.
Example: "If it rains, then the ground gets wet."
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Logical Arguments
Definition: A logical argument is a sequence of propositions aimed at demonstrating the truth of a conclusion.
Example:
Premises: "All men are mortal.
Socrates is a man. "
Conclusion: "Therefore, Socrates is mortal."
Structure of Logical Arguments:
Premises: Propositions that provide the basis for the argument.
Conclusion: The proposition that follows logically from the premises.
Definition: A proposition is a declarative sentence that is either true or false, but not both.
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Non-Examples
"What time is it?" (This is a question, not a declarative sentence.)
"Close the door." (This is a command, not a declarative sentence.)
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