Answer to Question #284172 in Discrete Mathematics for Derek

Question

Write the converse, inverse, and contrapositive of the following conditional

propositions. (Hint: If applicable, write each conditional proposition in standard

form first.)

a. Rose may graduate if she has 120 hours of OJT credits.

b. A necessary condition for Bill to buy a computer is that he obtains

P20,000.

c. A sufficient condition for Katrina to take the algorithms course is that

she passes discrete mathematics.

d. The program is readable only if it is well-structured.

Answer 1

Solution:

a)

Standard form:

If Rose has 120 hours of OJT credits then she may graduate.

converse:

If Rose may graduate then she has 120 hours of OJT credits.

Inverse:

If Rose do not have 120 hours of OJT credits then she may not graduate .

Contrapositive:

If rose may not graduate then she do not have 120 hours of OJT credits.

b)

Standard form:

If Bill buy a computer then he obtains P20,000.

converse:

If Bill obtains P 20,000 then he buys a computer.

Inverse:

If Bill do not buy a computer then he does not obtain P 20,000.

contrapositive:

If Bill do nat obtain P 20,000 then he does not buy a computer.

c)

Standard form:

If katrina passes discrete mathematics then she takes the algorithms course.

converse:

If Katrina takes the algorithms course then she passes discrete mathematics.

Inverse:

If katrina does not pass discrete mathematics then she does not take the algorithms course.

contrapositive:

If katrina does not take the algorithms course then she does not pass discrete mathematics.

d)

standard form:

If program is readable then it is well-structured.

converse:

If program is well structured then it is readable.

Inverse:

If program is not readable then it is not well-structured.

contrapositive:

If program is not well-structured then it is not readable.