We want to find S so ((A → B) ^ A) → S is a tautology. AB(A=B) ^ A S ((A= B) ^ A) => S TT TF F T F F (a) In order for ((A→ B) ^ A) → S to be a tautology, what must the truth values of S be? Include all possibilities.
We want to find S so ((A → B) ^ A) → S is a tautology. AB(A=B) ^ A S ((A= B) ^ A) => S TT TF F T F F (a) In order for ((A→ B) ^ A) → S to be a tautology, what must the truth values of S be? Include all possibilities.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:2. We want to find S so ((A = B)A A) = S is a tautology.
AB(A= B) ^ A
TT
TF
FT
FF
S
((A= B) A A) =→ S
(a) In order for ((A= B) ^ A) = S to be a tautology, what must the
truth values of S be? Include all possibilities.
(b) Write down two simple statements A and B. (They should be
statements whose truth value can be easily determined)
(c) Use your simple statements give an example, in ordinary language,
of (A = B) A A.
(d) Using your ordinary language statement of (A = B) A A, what
might you conclude?
(e) What does this suggest S should be?
(f) Verify that your choice of S makes ((A = B)AA) → Sa tautology.
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