Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**reconsideryouranswer****Member**- Registered: 2011-05-11
- Posts: 171

For the true-false problems for this thread, all cases for a particular

statement must be **true,** else it is deemed **false.** That is, I am not

presenting exercises in the always true/sometimes true/never true format.

1. Within the confines of the United States, the westernmost part of Virginia

lies farther west than the westernmost part of West Virginia.

Suppose there are sets of fair, 6-sided dice, but they do not necessarily have

the values of 1 through 6 once each on each face. Numbers other than

1 through 6 might be included, as well as certain sides could share the

same value. An example might be a die with these values, one per each face:

2, 2, 3, 4, 5, 8. The value of two or more dice thrown, such as A + A, is the sum

of the values of their top faces.

There are also sets of C dice and D dice with the above properties.

Dice X, Y, W, and Z are also like the above in properties, except that

they are nonspecific for the illustration below.

Given: One set of four fair, identically-numbered 6-sided dice and a different

set of four fair, identically-numbered dice. X > Y means that die X

has a greater chance of having a larger value than die Y upon tossing them.

W < Z means that die W has a greater chance of having a smaller value

than die Z when the dice are tossed.

2. (i)

If A > B, and A + A + A > B + B + B, then

A + A > B + B.

2. (ii)

If A + A < B + B and A + A + A + A < B + B + B + B, then

A + A + A < B + B + B

2. (iii)

If A + B > C + C, and A + B > D + D, then

A + B > C + D

"Lines" in the following refer to straight lines in the xy-plane.

Also, I am using "asymptote(s)" here to be only lines

(horizontal, vertical or oblique) instead of the nonlinear

asymptotes that exist for other certain functions.

3. (i)

Given: A certain function approaches a line and gets ever closer

to it without intersecting it.

That line is an asymptote to that function.

3. (ii)

A function does not interect its asymptote(s).

3. (iii)

The same function cannot have a horizontal asymptote

and an oblique asymptote.

4. In the vertical line test, where there is a graph of a relation

that is not a function, the vertical line crosses at two or more

points for each corresponding x-value in the relation's domain.

5. For any pair of perpendicular lines, the value of one slope

multiplied by the value of the other slope equals -1.

6. In plotting three points for a certain intended line (on graph paper,

for example) in the xy-plane, if a person has three points

that line up, then that person knows that those three points

lie on the same intended line.

7.

8. There is a movie starring Jim Carrey and Kate Winslet

involving erasing of certain memories.

The title of this movie is one of the choices below, true or false:

"Spotless Mind of the Eternal Sunshine"

"Spotless Eternal Sunshine of the Mind"

"Spotless Sunshine of the Eternal Mind"

"Spotless Eternal Mind of the Sunshine"

"Eternal Spotless Mind of the Sunshine"

"Eternal Spotless Sunshine of the Mind"

"Eternal Mind of the Spotless Sunshine"

"Sunshine of the Spotless Eternal Mind"

"Sunshine of the Eternal Spotless Mind"

"Sunshine Eternal of the Spotless Mind"

"Sunshine Spotless of the Eternal Mind"

"Mind of the Eternal Spotless Sunshine"

"Mind of the Spotless Eternal Sunshine"

"Mind Spotless of the Eternal Sunshine"

"Mind Eternal of the Spotless Sunshine"

9. In the same plane, two distinct quadrilaterals can intersect

each other in no more than eight distinct places.

10. There are no infinite subsets (all members distinct) of the set

of irrational numbers such that they can be put into a one-to-one

correspondence with the set of positve integers.

11. Given: a, b, c, d belong to the Real numbers, where a, b, c, d > 1.

12. A polyhedron exists that has seven edges.

Signature line:

I wish a had a more interesting signature line.

Offline