Discrete Mathematics Answers

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 A and B are two non-empty sets such that A x B = B x A, show that A=B

If A is the set of triangles in a plane then prove that the relation R defined by "a is similar to b" is an equivalence relation.

show that ((p v !q)→((p v !p)-r)→(q→r) is a tautology.

Let E = {2, 4, 6, …}. Then prove that (E, +) is a semigroup, where + is usual addition.

If A is the set of triangles in a plane then prove that the relation R defined by “a is similar to b ” is an equivalence relation?

i need someone to calculate CPI starting from £0.25 all the way to £2.00 over 1000views starting from £0.25 all the way to £2.00 for example if you charge 1p for one impression and receives 1000 impressions you will receive £1 i want you to start with as low rate of £0.25p for 1000 impression all the way up to how much i will earn with £0.25 for 1000000000000000 impressions and the same for 26p 27p 28p all the way to £2 can this be done on excell aswell please

Let E = {2, 4, 6, …}. Then prove that (E, +) is a semigroup, where + is usual addition.

prove that the any restaurant bill of $n,n>or=5 be paid exactly using only $2 and $5 bills