mathematical structures hw1

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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 “The pencil is green or today is not Friday” would be written symbolically as 𝑞 ∨𝑝̅ .) a. Today is not Friday, but 2 ≥ 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 ≥ 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 (𝑎 ∨𝑏) → (𝑏 ∨𝑐) is false. (Write “True” or “False” in the blank provided.)

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

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