lesson 1 and 2 discrete maths 100% correct

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1) Determine which of the following sentences are propositions. Give a brief reason for your

answer.

(a) Seven is two more than five.

(b) Stop whining!

(c) There is a black hole at the center of every galaxy.

(d) This sentence has five words.

(2) Construct truth tables for each of the following.

(a) ¬q −→ p.

(b) (p ∨ q) −→ r. (You will need eight rows for this one.)

(3) Let s be the proposition It is snowing, f be the proposition It is below freezing, and r be It

is raining. Convert the following English sentences into statements using the symbols s, f,

r and logical connectives.

(a) It is snowing or it is not below freezing.

(b) If it is snowing, then it is not raining and it is below freezing.

(4) Use a truth table to verify the equivalence: p −→ ¬q ≡ ¬p ∨ ¬q.

Explain why the truth table shows that the propositions are equivalent.

(5) Use a truth table to show that the statements p −→ (q −→ r) and (p −→ q) −→ r

are not logically equivalent.

Explain why the truth table shows that the propositions are not equivalent.



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    • 6 years ago
    lesson 1 and 2 discrete maths 100% correct
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