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Write the converse, inverse, and contrapositive of the following statement.
If he studies, then he will go to college.
Concept: undefined >> undefined
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
Concept: undefined >> undefined
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With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
Concept: undefined >> undefined
With proper justification, state the negation of the following.
(p → q) ∧ r
Concept: undefined >> undefined
Construct the truth table for the following statement pattern.
(p ∧ ~ q) ↔ (q → p)
Concept: undefined >> undefined
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~q)
Concept: undefined >> undefined
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
Concept: undefined >> undefined
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(q ∧ r)
Concept: undefined >> undefined
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
Concept: undefined >> undefined
What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.
Concept: undefined >> undefined
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]
Concept: undefined >> undefined
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)
Concept: undefined >> undefined
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]
Concept: undefined >> undefined
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]
Concept: undefined >> undefined
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
Concept: undefined >> undefined
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Concept: undefined >> undefined
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Concept: undefined >> undefined
Using the truth table, prove the following logical equivalence.
p ∧ (~p ∨ q) ≡ p ∧ q
Concept: undefined >> undefined
Using the truth table, prove the following logical equivalence.
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
Concept: undefined >> undefined
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
Concept: undefined >> undefined
