Define the following propositions e: I will return to college, J: I will get a j

Question

Define the following propositions e: I will return to college, J: I will get a job. Translate the following English sentence into logical expressions using the definitions above: a. If I do not return to college then I will get a job b. I am not getting a job, but I am still not returning to college. Which of the following conditional statements are true and why? a. Pigs can whistle if and only if donkeys can fly. b. If 5 is not a prime number, then pigs can whistle. Give the inverse, converse, and contrapositive for each of the following statements: a. If he trains hard for the race, then he will finish the race. b. If you eat your vegetables then you can have some dessert.

Explanation / Answer

Ques 7.

a )

x : I will get a job.

y : If i will not return to the college.

b )

x : I am not returning to the college.

y : I am not getting the job.

Ques 8. Option (b) is correct.

If 5 is not a prime number, then pigs can whistle.

Because, it is a unversal truth and a thing which cannot be denied that 5 is a prime number. And by this the actual hypothesis which is pigs can whistle becomes wrong thereby satisfying the whole condition.

Ques 9.

(a) If he trains hard for the race, he will finish the race.

Converse - If he will finish the race, then he trained hard for the race.

Inverse - If he will not train hard for the race, he will not finish the race.

Contrapositive - If he did not finish the race, then he did not trained hard for the race.

(b) If you eat your vegetables then you can have some desert.

Converse - You can have some desert if you will eat your vegetables.

Inverse - If you will not eat your vegetables, you will not have desert.

Contrapositive - If you will not have desert, you have not eaten your vegetables.

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