The Probability of the Truth on a Truth Table

In symbolic (or mathematical) logic the truth table is used to establish the truth or falsity (falsehood) of both simple and compound statements (or arguments). However, the use of the term “truth table” falsely suggests that all arguments through the table are true. It is known that the table contains both true and false arguments. So the use of “truth table” is indiscriminate. Consequently, this study was focused on solving this problem by finding out the probability of having a true argument associated with every one of the four binary proposition connectives- “and”, “double implication” “inclusive v”, single implication”  used in the arguments. The obtained probabilities are ordered as 1/4, ½ and ¾ respectfully for “and”, “double implication”, and (“inclusive v” and “single implication”). So the “truth tables” are discriminately decomposed into “falsehood tables”, “neutral tables” and “truth tables” at probabilities of ¼, ½ and ¾ respectively. These probabilities are independent of the number of statements, n, greater than unity

Comparing Two Examination Results using Means of Sample Means and Control Charts

Some examination candidates submit their scripts first, sometimes, for recognition as being brilliant, and some do for not knowing what to write. However, some equally submit last because they want to dot i’s and cross t’s. The objective of this research is to compare the results of both the earliest and latest submissions with the aim of finding out whether or not there is a significant difference between the two. The examination results of students of the Departments of Accounting, Business Administration and Industrial Relations and Personnel Management of the Faculty of Business Administration and the Department of Mathematics, Faculty of Science,  University of Lagos were  compared using means of sample means and two statistical quality control charts. The results showed that, generally, the early submissions seemed to be an indication of being more brilliant than the last submissions in the Faculty of Business Administration. In the Mathematics Department, however, the last to submit appeared to be more brilliant. Keywords:measures of brilliance, statistical quality control, two-sample test, ordered-data-control charts,  time sequence of exam-script submission, competition assessmen