Suppose A1, A2, A3,... is a sequence of formulae. Does the following tautological implication hold? {Am : ne N} Fraut A15 → A10 O a. Yes, if A10 is a tautology. O b. Yes, but only if A10 is a contradiction. O. No, it does not hold. O d. Yes, it does. O e. Yes, if A15 is a tautology.

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Suppose A1, A2, A3,... is a sequence of formulae. Does the following tautological implication hold?
{Am : n € N} Faut A15 → A10
O a. Yes, if A10 is a tautology.
O b. Yes, but only if A10 is a contradiction.
O c. No, it does not hold.
O d. Yes, it does.
O e. Yes, if A15 is a tautology.
Suppose A = (B V C) is a r-theorem. Which one of the following formulae is also a r-theorem by the Leibniz
rule?
O a. C v (B → C) = C ^ A
O b. C v (A v C) = C v B
O c. A V B = (A v (B v C))
O d. C v (B v C) = C v A
O e. (CA B) V A = (A v A)
Transcribed Image Text:Suppose A1, A2, A3,... is a sequence of formulae. Does the following tautological implication hold? {Am : n € N} Faut A15 → A10 O a. Yes, if A10 is a tautology. O b. Yes, but only if A10 is a contradiction. O c. No, it does not hold. O d. Yes, it does. O e. Yes, if A15 is a tautology. Suppose A = (B V C) is a r-theorem. Which one of the following formulae is also a r-theorem by the Leibniz rule? O a. C v (B → C) = C ^ A O b. C v (A v C) = C v B O c. A V B = (A v (B v C)) O d. C v (B v C) = C v A O e. (CA B) V A = (A v A)
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