Practice Tautology Implication (7.5.2) - Tutorial 1: Part II - Discrete Mathematics

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6 sample questions

Question 1.
Define functional completeness in your own words.
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Consider how operators like AND, OR, and NOT interact.
Question 2.
True or False: A tautology is always satisfiable.
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Think about the definition of a tautology.
3Question 3.
Which of the following describes a tautology?
- It is always false
- It is always true
- It depends on the context
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Reflect on the nature of tautological statements.
4Question 4.
True or False: The statement 'p ∨ ¬p' is a tautology.
- True
- False
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Think of both possible truth values for 'p'.
Question 5.
Prove that conjunction and negation are functionally complete by expressing disjunction using only these operators.
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Refer to De Morgan's laws for guidance.
Question 6.
Construct a truth table for the expression '¬(p ∧ q)' and demonstrate that it is equivalent to 'p ∨ q'.
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Break down the expression and assess each truth value.

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