applying two definitions of the union of if-events, p. grzegorzewski gave two generalizations of the inclusion-exclusion principle for if-events.in this paper we prove an inclusion-exclusion principle for if-states based on a method which can also be used to prove grzegorzewski's inclusion-exclusion principle for probabilities on if-events.finally, we give some applications of this principle by...

Safety standards (e.g., ISO 26262) define safety life-cycles to be adopted for the development of safety-critical systems. Professionals (i.e., safety engineers, safety managers, and, more broadly safety cultureaware personnel) who are responsible of the development of such systems can be, in turn, considered as safety-critical systems. Coursemodules aimed at forming such professionals are crit...

Sample size calculations require specification of the treatment effect, but what if this is not known? Two-stage tests use the first stage to estimate the treatment effect and modify the sample size accordingly. The purpose of this paper is to unify the theory of two-stage testing based on treatment effect. The conditional error function approach of Proschan and Hunsberger (1995) is shown to be...

In standard arithmetic, if we, e.g., accidentally add a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x+ y. In this paper, we prove the following two results: • First, a similar possibility to invert (undo) addition holds for fuzzy numbers (although in case of fuzzy numbers, we cannot simply undo addition by subtracting y from the sum). ...

Abstract The present research was conducted to compare the efficiency of 3 groups of ESP instructors: content teachers, language teachers, and professional ESP teachers. The main question was aimed to investigate whether there was a significant difference between the 3 mentioned groups of ESP teachers and if there was, who was more qualified to teach ESP. To find the answer, a questionnaire was...

Abstract The present research was conducted to compare the efficiency of 3 groups of ESP instructors: content teachers, language teachers, and professional ESP teachers. The main question was aimed to investigate whether there was a significant difference between the 3 mentioned groups of ESP teachers and if there was, who was more qualified to teach ESP. To find the answer, a questionnaire was...

Since the emergence of the process-oriented approach to second language writing instruction two main questions have been what and how error feedback should be given to the students. The question of whether teachers should provide feedback on grammar in the writing assignments of English as a foreign language students, and if so how, has been a matter of considerable debate in the field of secon...