# Answer to Question #13991 in Discrete Mathematics for Tobia Tohotoa

Question #13991

1) Use a truth table to determine whether the argument given below is valid:

If it is a wild animal, it is dangerous. If it is dangerous, it will hurt

you. However, it is not dangerous. Therefore, it is not a wild animal.

2) Let the domain be {1,2,3,4,5} and P(x) be the proposition x < x2. Determine the truth value of

a) \forall x P(x)

b) \exists x P(x)

a) \forall x\neg P(x)

b) \exists x\neg P(x)

3) Prove that for all integers a, b, n: if n = a + b, then a < n/2 or b < n/2 .

(Hint: use proof by contrapositive)

4) Prove that for every set S, Ø \subseteq S.

Hint: Use vacuous proof.

If it is a wild animal, it is dangerous. If it is dangerous, it will hurt

you. However, it is not dangerous. Therefore, it is not a wild animal.

2) Let the domain be {1,2,3,4,5} and P(x) be the proposition x < x2. Determine the truth value of

a) \forall x P(x)

b) \exists x P(x)

a) \forall x\neg P(x)

b) \exists x\neg P(x)

3) Prove that for all integers a, b, n: if n = a + b, then a < n/2 or b < n/2 .

(Hint: use proof by contrapositive)

4) Prove that for every set S, Ø \subseteq S.

Hint: Use vacuous proof.

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