Can someone plzzz explain. Why do you only need a single counterexample to show that a conditional statement is false?

Q1) jin loves carrot yesterday she ate ½ of here carrots and today she ate 2/3 of the remaining carrots. she then discover that she has 12 carrots left. yesterday she must has started with carrots? a)36 b)48 c)60 d)72

Tod does not have any cookies. david gives jeff 8 cookies. then he splits half of the cookies he has left with tod. david let’s c represent the number of cookies that he starts with. he finds the number of cookies that tod has is 1/2 the difference of c and 8. write an expression to represent the number of cookies that tod has.

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.