Discussion
Find out the correct match :
Answer: A
The correct match is Tautology : ~ (p . ~ p).
~ (p . ~ p), the law of non-contradiction, is true whatever the truth value of p: p . ~ p is always false, so its negation is always true.
The others are mismatched. p ∨ ~ p, the law of excluded middle, is also a tautology, not a contingent formula. The law of double negation is p ≡ ~ ~ p, and the printed '~ (~ ∧ p)' is not even well formed. The rule shown in option D, inferring φa from (∃x) φx, is existential instantiation; existential generalisation goes the other way, from φa to (∃x) φx.
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