Discrete Math

2. Find a counterexample to the statement nonzero integers n, n^2 4/n is not an integer.

3. Find a negation for each statement.

(a) bicycles b, b has two wheels.

(b) a tree t such that t does not lose its leaves in the fall.

(c) dogs d, if d sits, then d gets a treat.

(d) x R, if x 2 4 < 0, then 2 < x < 2.

4. For each statement, write the contrapositive, converse, and inverse.

(a) dogs d, if d sits, then d gets a treat.

Contrapositive:

Converse:

Inverse:

(b) x R, if x 2 4 < 0, then 2 < x < 2.

Contrapositive:

Converse:

Inverse:

5. Let D = {78, 34, 26, 15, 11, 55, 62, 63, 74, 92}. Determine which of the following statements are true and which are false. Provide a counterexample for those statements which are false. (Hint: If the statement is false, write out the negation to know what a counterexample should be like.)

(a) x D, x + 1 6 D

(b) x D, if x < 20, then x is even.

(c) x D, if x is even, then x < 20.

(d) x D, if the tens digit of x is 4, then x < 100.

(e) x D, if the ones digit of x is 7, then x > 100.