Question

Q:Q: There exists a real number nn such that n2>100n2>100 implies n≤10n≤10 and n>0n>0
R:R: If Tom is Ann's father then Jim is her uncle and Sue is her aunt and Mary is her cousin.

In English, what are the negations, converses, and contrapositives of QQ and RR? You do not need to justify the correctness of the statements.

Answer 1

There exists a real number such that $n^2>100$ implies
10
and .

Negation: There does not exist a real number such that $n^2>100$ implies
10
and .
Converse: There exists a real number such that
10
and implies $n^2>100$ .
Contrapositive: There exists a real number such that or $n\leqslant 0$ implies $n^2\leqslant 100$ .

If Tom is Ann's father then Jim is her uncle and Sue is her aunt and Mary is her cousin.

Negation: Tom is Ann's father and Jim is not her uncle or Sue is not her aunt or Mary is not her cousin.
Converse: If Jim is Ann's uncle and Sue is her aunt and Mary is her cousin then Tom is her father.
Contrapositive: If Jim is not Ann's uncle or Sue is not her aunt or Mary is not her cousin then Tom is not her father.