Let p, q, and r be the propositions. p : You have the flu. q : You miss the final examination. r : You pass the course. Express each of these propositions as an English sentence. a) p → q
b) ¬q ↔ r
c) q → ¬r
d) p ∨ q ∨ r
e) (p → ¬r) ∨ (q → ¬r)
f ) (p ∧ q) ∨ (¬q ∧ r)

a) If you have the flu then you miss the final examination, b) You do not miss the final examination if and only if you pass the course, c) f you miss the final examination then you do not pass the course, d) Either you have the flu or you miss the final examination or you pass the course, e) If you have the flu then you do not miss the final examination or if you miss the final examination then you do not pass the course, f) You have the flu and you miss the final examination or you do not miss the final examination and you pass the course.

Step-by-step explanation:

Let be You have the flu, You miss the final examination and You pass the course.

a) If you have the flu then you miss the final examination.

b) You do not miss the final examination if and only if you pass the course.

c) If you miss the final examination then you do not pass the course.

d) Either you have the flu or you miss the final examination or you pass the course.

e) If you have the flu then you do not miss the final examination or if you miss the final examination then you do not pass the course.

f) You have the flu and you miss the final examination or you do not miss the final examination and you pass the course.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

its 4 because 2 times 2 is 4, if you double the number two you get four