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Q1. Determine if the Expression is a Tautology

Expression: ¬q → (¬q ∧ p) → ¬q

To determine whether the expression is a tautology, we must check if it is true for all possible truth values of q and p.

1. Construct the truth table:

q	p	¬q	¬q ∧ p	(¬q ∧ p) → ¬q
T	T	F	F	T
T	F	F	F	T
F	T	T	T	T
F	F	T	F	T

2. Analyze the expression ¬q → ((¬q ∧ p) → ¬q):

• Since the expression (¬q ∧ p) → ¬q is true for all combinations of q and p, ¬q → (¬q ∧ p) → ¬q is also always true.

Conclusion: The expression is a tautology.

Would you like to go through the next question, or do you need a more detailed explanation on this one?

Here are some related questions to consider:

1. What is a tautology in logic?
2. How do you construct a truth table?
3. What does the inverse of a logical statement mean?
4. What is the converse of a logical statement?
5. What is the contrapositive of a logical statement?
6. How do you prove that a set is a subset of another set?
7. What is the significance of the universal set in set theory?
8. How do you find the binary expansion of a hexadecimal number?

Tip: When determining if a logical statement is a tautology, the key is to check if the statement is true for all possible truth values of its components.