How to express these in terms of predicates & quantifiers :
- Some properties are tautologies
- The negation of a contradiction is a tautology
- The dis junction of two contingencies can be a tautology.
- The conjunction of two tautologies is a tautology.
I could find the answer from the answer key in this sequence as:
- $\exists xT(x)$
- $\forall x(C(x)\rightarrow T(\neg x)) $
- $\exists x\exists y(\neg T(x)\wedge \neg C(x) \wedge \neg T(y) \wedge \neg C(y) \wedge T(x\vee y)) $
- $\forall x\forall y((T(x) \wedge T(y)) \rightarrow T(x\wedge y))$
From Rosen 5th edition
And not at all able to know how did he arrive at this answer
Can anyone help ? !!
Thanks in advance