Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem5

Video Transcription

Question number five. The CEO of a company said every employee in our company is at least 25 years old. It turned out that the CEO was wrong. It  necessarily follows that and then we have five statements here that are possible negations of the CEO's statement. So let's identify the clauses  here in the statement and mathematically write them down and then negate both of them. So we have two clauses. First of all it's a universal quantifier dealing  with employees, every employee, and then a statement about the employees, about their age, that each is at least 25 years old. So for the first clause here, let me  just label that here one and here I'll label this one two, we have one says that every employee and then two says that we have at least 25 years of age and then  the negation here would be the opposite of every means at least one. So not everybody, one person does not enjoy this property and the negation of  the second statement would be simply less than 25. And so now we can check which of the five statements is equivalent to our negation and a we have  every employee is exactly 25 years old so this does not have the correct negation of the first statement. It is in fact still keeping the original, it  hasn't been negated at all. Statement B here says every employee is older than 26 years and again the first clause has not been negated. Statement C says no  employee is 25 years old and again the first clause has not been negated correctly. The negation of every is not none but at least one. In statement E we  have a correct negation of the first statement at least one employee and then an incorrect negation of the second. It should say not exactly  26 years old but less than and 26 should be 25. So that leaves us with statement D over here. The first clause is correctly negated we have instead of every at  least one and then the second clause is correctly negated instead of at least 25 years old we have exactly less than 25. So these line up, these match, we have  correct negations and so we choose D here as the answer.

Video Summary

The video transcript analyzes a logical problem based on a CEO's incorrect statement that every company employee is at least 25 years old. The task is to find the negation of this statement among five options. The negation involves stating that at least one employee is less than 25 years old. The transcript concludes that option D correctly negates both parts of the CEO's statement, specifying that at least one employee is indeed younger than 25 years, thus solving the problem accurately.

Keywords

logical problem

CEO statement

negation

employees

age analysis