(I) The invalidation of the principal proclamation is ‘the number\[~x\] is a levelheaded number’.

This is same as the second assertion since, in such a case that a number is certainly not a silly number then the number is a levelheaded number

Consequently, the given assertions are refutations of one another

(ii) The refutation of the main assertion is ‘the number \[x\]is certifiably not a judicious number. This implies that the number \[x\]is an unreasonable number which is same as the subsequent assertion.

Consequently, the given assertions are nullifications of one another