This class Write the following statements in symbolic form o

This class..

Write the following statements in symbolic form of implication (i.e., \"p q\", and define clearly what p is and what q is): David will go ski at 4pm only if he finishes the homework by then; Carrie won\'t help snow removal unless she is sure of a sunny day today; A minimum grade of B+ is necessary for taking course CMPUT 204; Ada is smart or she is happily married. Write negations, converses, inverses and contrapositives of the implication statements, that you have worked out in the above Question 9, in English. Make sure your answers are easy to read.

Solution

9).

a).

p = he finishes the homework by 4 pm

q = david will go ski at 4 pm

b).

p = she is sure of a sunny day today

q = Carrie will help snow removal

c).

p = you can take course CMPUT 204

q = you have a minimum grade of B+

d).

p = Ada is not smart

q = she is happily married

(beacuse p -> q == ~p v q)

10).

negations:

p -> q has negation p AND ~q

a). David finishes the homework by 4 pm and he will not go ski at 4 pm

b). Carrie is sure of a sunny day today and Carrie will not help snow removal

c). Rou can take course CMPUT 204 and you do not have a minimum grade of B+

d). Ada is not smart and she is not happily married

converse:

p -> q has converse q -> p

a). David finishes the homework by 4 pm only if he goes ski at 4 pm

b). Carrie is sure of a sunny day today unless she helps snow removal

c). you can take course CMPUT 204 only if you have a minimum grade of B+

d). she is not happily married or Ada is not smart

inverse:

p -> q has inverse ~p -> ~q

a). if david doesn\'t finish the homework by 4 pm then he will not go ski at 4 pm

b). if Carrie is not sure of a sunny day today then she will not help snow removal

c). if you can not take course CMPUT 204 then you do not have a minimum grade of B+

d). if Ada is smart then she is not happily married

contrapositive:

p -> q has contrapositive ~q -> ~p

a).

If David will not go ski at 4 pm then he has not finished the homework by 4 pm

b).

If Carrie will not help in snow removal then she is not sure of a sunny day today

c).

If you don\'t have a minimum grade of B+ then you can\'t take course CMPUT 204

d).

If Ada is not happily married then she is smart