Practice Final Question (7.8) - Tutorial 1: Part II - Discrete Mathematics

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6 sample questions

Question 1.
What is a functionally complete set of logical operators?
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Think about the operators you commonly use.
Question 2.
Convert the expression p → q to an expression using only negation and disjunction.
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Use the implication identity.
3Question 3.
What is the definition of a functionally complete set of logical operators?
- A set that can express some logic statements.
- A set that can express every logical statement.
- A set that is always true.
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Consider what 'every' means in this context.
4Question 4.
True or False: You need both AND and OR to create a functionally complete set.
- True
- False
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Think about alternative sets of operators.
Question 5.
Create a truth table to demonstrate the equivalence between p ∧ q and ¬(¬p ∨ ¬q).
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Make sure to cover all possible truth values for p and q.
Question 6.
Show that a set of logical operators including only NOT and NOR can still express all logical propositions.
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Start by transforming implications first.

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