# mathematical structures hw1

super simple math hw.

1. Let p, q, and r represent the following propositions: p: Today is Friday q: The pencil is green. r: 2 < 5

Write each of the following statements symbolically, putting your answer into the space provided.

(As an example, the statement â€œThe pencil is green or today is not Fridayâ€ would be written symbolically as ð‘ž âˆ¨ð‘Ì… .) a. Today is not Friday, but 2 â‰¥ 5. _______________ b. 2 < 5 is a sufficient condition for the pencil to be green. _______________

c. The pencil is green unless today is Friday. _______________ d. In order for the pencil to be green and today to be Friday, it is necessary that 2 â‰¥ 5. _______________ e. The pencil is not green, and 2 < 5 implies that today is Friday. _______________

f. The pencil is green only if today is not Friday. _______________

g. Today is Friday if and only if the pencil is not green. _______________

2. Determine the truth values of a, b, and c if (ð‘Ž âˆ¨ð‘) â†’ (ð‘ âˆ¨ð‘) is false. (Write â€œTrueâ€ or â€œFalseâ€ in the blank provided.)

a must be _______, b must be _______, and c must be _______.