Answer
a) Let the domain be the collection of all propositions.
Let P(x) means " x is a tautology".
$$\exists x P(x)$$
b) Let the domain be the collection of all propositions.
Let P(x) means " x is a tautology" and Q(x) means that " x is a contradiction".
$\neg x$ means the contradiction of proposition x.
$$\forall x (Q(x) \rightarrow P(\neg x))$$
c) Let the domain be the collection of all propositions.
Let P(x) means " x is a tautology" and R(x) means that " x is a contingency".
$$\exists x \exists y((R(x) \land R(y))\rightarrow P(x\lor y))$$
d)Let the domain be the collection of all propositions.
Let P(x) means " x is a tautology".
$$\forall x \forall y((P(x) \land P(y))\rightarrow P(x\land y))$$
Work Step by Step
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