Write the converse, inverse, and contrapositive of the statements. (a) ~p → ~q Converse: p → ~q~q → p ~q → ~pq → pp → q Inverse: p → ~q~q → p ~q → ~pq → pp → q Contrapositive: p → ~q~q → p ~q → ~pq → pp → q (b) ~t → s Converse: t → ~s~s → t t → ss → ~t~s → ~t Inverse: t → ~s~s → t t → ss → ~t~s → ~t Contrapositive: t → ~s~s → t t → ss → ~t~s → ~t

Write the converse, inverse, and contrapositive of the statements. (a) ~p → ~q Converse: p → ~q~q → p ~q → ~pq → pp → q Inverse: p → ~q~q → p ~q → ~pq → pp → q Contrapositive: p → ~q~q → p ~q → ~pq → pp → q (b) ~t → s Converse: t → ~s~s → t t → ss → ~t~s → ~t Inverse: t → ~s~s → t t → ss → ~t~s → ~t Contrapositive: t → ~s~s → t t → ss → ~t~s → ~t

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Write the converse, inverse, and contrapositive of the statements.

(a)

~p → ~q

Converse:

p → ~q~q → p ~q → ~pq → pp → q

Inverse:

p → ~q~q → p ~q → ~pq → pp → q

Contrapositive:

p → ~q~q → p ~q → ~pq → pp → q

(b)

~t → s

Converse:

t → ~s~s → t t → ss → ~t~s → ~t

Inverse:

t → ~s~s → t t → ss → ~t~s → ~t

Contrapositive:

t → ~s~s → t t → ss → ~t~s → ~t

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