$(20$ points$)$

Write the negation of the statement in good English. Don$$t write $$It is not true that $....$

$($a$)$ Some bananas are yellow.

$($b$)$ All integers ending in the digit $7$ are odd.

$($c$)$ No tests are easy.

$($d$)$ Roses are red and violets are blue.

$($e$)$ Some skiers do not speak Swedish.

Solution:

$9.(10$ points$)$ Translating English to Predicate Logic

Suppose the variable x represents students and y represents courses, and:

U $($y$)$: y is an upper$-$level course M $($y$)$: y is a math course F $($x$)$: x is a freshman

B$($x$)$: x is a full$-$time student T $($x$,$ y$)$: student x is taking course y$.$

Write the statement using these predicates and any needed quantifiers.

$($a$)$ Eric is taking CSCI $2625.$

$($b$)$ All students are freshmen.

$($c$)$ Every freshman is a full$-$time student.

$($d$)$ No math course is upper$-$level.