Discrete Mathematics Answers

when is a set said to be poset

prove that 1^2+3^2+5^2+...+(2n+1)^2 = (n+1)(2n+1)(2n+3)/3 whenever n is a nonnegative integer.

prove that every subgraph of a planar graph is planar

The universal set is the set of the integers from 1 to 25, both inclusive. The sets P, Q and R are defined as

P= {p:p is a multiple of 2}
Q= {q:q is a multiple of 3}
R= {r:r is a multiple of 9}

Illustrate the relationship of P, Q and R in a Venn diagram and mark the numbers in each region.

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.

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.