$2.$ Let P$($x$,$ y$)$ be the statement $$x has been a participant in y$.$ Express each of the following

sentences in terms of P$($x$,$ y$),$ quantifiers, and logical connectives, where the universe for x is

the set of all students at PSU and for y is the set of all school events. $(10$ pts$)$

$($a$)$ There is a student at PSU who has been a participant in a school event.

$($b$)$ No student at PSU has ever been a participant in a school event.

$($c$)$ There is a student at PSU who has been a participant in graduate ceremony and spelling

bee.

$($d$)$ Every school event has had a student from PSU as a participant.

$($e$)$ At least two students from PSU have been participants in spelling bee.

Answer:

CMPSC $360,$ Fall $2024,$ HW $32$