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Virginia Math
Discrete Mathematics: Logical Reasoning
Use Venn diagrams to codify and solve logic problems.
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Express logical statements in symbolic form.
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Represent a conditional statement as its converse, inverse, and contrapositive.
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Describe how symbolic logic can be used to map the processes of computer applications.
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Construct a truth table to display all possible input combinations and their outputs.
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Identify the rules of inference and model basic logical statements including De Morgan’s Law.
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Apply logical reasoning to model contextual situations and make decisions.
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Apply informal logical reasoning to contextual problems (e.g., predicting the behavior of software, solving puzzles).
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Outline the basic structure of a proof technique (e.g., direct proof, proof by contradiction, induction).
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Deduce the best type of proof for a given problem.
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Use the rules of inference to construct direct proofs and proofs by contradiction.
Construct induction proofs involving summations and inequalities.
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Use a truth table to prove the logical equivalence of statements.
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Explain basic properties of Boolean algebra: duality, complements, and standard forms.
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Represent verbal statements as Boolean expressions.
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Apply Boolean algebra to prove identities and simplify expressions.
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Generate truth tables that encode the truth and falsity of two or more statements.
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Explain the operation of discrete logic gates.
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Describe the relationship between Boolean algebra and electronic circuits.
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Analyze a combinational network using Boolean expressions.
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Design simple combinational networks that use NAND (AND followed by NOT), NOR (OR followed by NOT), and XOR (exclusive-OR) gates.
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Compare and contrast inductive and deductive reasoning.
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Explain the relationship between weak and strong induction.
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Construct induction proofs involving a divisibility argument.
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Prove the Binomial Theorem through mathematical induction.
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