0 Mathematical Analysis Please provide complete and correct

0. Mathematical Analysis. Please provide complete and correct mathematical solution done on computer or by hand. Please, emphasis on correct solution. This is all the information provided. Thank you very much.

3. Write the contrapositive, converse, and inverse of each of the following implications (a) If all roses are red, then violets are blue (b) If roses are red, then all violets are blue c) H is normal if H is not regular. (d) If K is closed and bounded, then K is compact. 4. Translate \"N5. A subset of N which contans 1. and which contains n 1 whenever it contains n, must equal N.\" mto set notaton and math logic

Solution

Condition: p. Implies. Q

Contrapositive: ~q. Implies ~ p

Converse. : q. Implies. P

Inverse. : ~p. Implies. ~q

A) contrapositive: if Violets are not blue. Then. All Roses are. Not red

Converse : if violets are blue then all roses are red

Inverse: if all roses are not red then violets are not blue

B) contrapositive: if all violets are not blue then roses are not red

Converse: if all violets are blue then roses are red

Inverse: if roses are not red then all violets are not blue

C)contrapositive: if H is not normal then H is regular

Converse: if H is normal then H is not regular

Inverse: if H is regular then H is not normal

D)contrapositive: if K is not compact then K is not closed and bounded

Converse: if K is compact then K is closed and bounded

Inverse: if K is not closed and bounded then K is not compact