VERBAL IF-THEN'S For each of the following, do your best to figure out if the statement is true or false. Give an explanation (or argument) justifying why you think what you think. NOTE: Each of the following refers to "a number" or "numbers". They are general statements. So, if there is any number (or numbers) for which it's false, then the statement is false. In other words, if you are thinking "that's true in some cases (or perhaps even many cases), but it's not true in all cases," then the statement is false. Warning: The word "number" does not mean "integer" or "positive integer". All integers are numbers, but not all numbers are integers. Integers are numbers like -13, -4, 0, 27, and 132. Non-integers are numbers like 2.61, - 5.8, and 55/9. The first of these is between the consecutive integers 2 and 3. The second is between -6 and -5. The third is between 6 and 7. So if you are going to test the statements by choosing a number or numbers to test it with, do not limit yourself to the simplest case, which is positive integers only. Many things are true for positive integers that are not true in general. 1. If you add two numbers together and square the result, then you'll get the same thing as squaring the two numbers and adding those two results. (Note: "Squaring" something means to multiply it by itself. For example, squaring 8 yields 8x 8 = 64.) 2. If you multiply a number by 6, add 11 to that result, and divide that result by 2, then you'll get the same thing as you would have if you had simply multiplied the number by 3 and added 11 to that result. 3. If you have 17 identical objects in a box and you add 4 more of the same exact object type to the box, then the box will now contain 21 of those objects.
VERBAL IF-THEN'S For each of the following, do your best to figure out if the statement is true or false. Give an explanation (or argument) justifying why you think what you think. NOTE: Each of the following refers to "a number" or "numbers". They are general statements. So, if there is any number (or numbers) for which it's false, then the statement is false. In other words, if you are thinking "that's true in some cases (or perhaps even many cases), but it's not true in all cases," then the statement is false. Warning: The word "number" does not mean "integer" or "positive integer". All integers are numbers, but not all numbers are integers. Integers are numbers like -13, -4, 0, 27, and 132. Non-integers are numbers like 2.61, - 5.8, and 55/9. The first of these is between the consecutive integers 2 and 3. The second is between -6 and -5. The third is between 6 and 7. So if you are going to test the statements by choosing a number or numbers to test it with, do not limit yourself to the simplest case, which is positive integers only. Many things are true for positive integers that are not true in general. 1. If you add two numbers together and square the result, then you'll get the same thing as squaring the two numbers and adding those two results. (Note: "Squaring" something means to multiply it by itself. For example, squaring 8 yields 8x 8 = 64.) 2. If you multiply a number by 6, add 11 to that result, and divide that result by 2, then you'll get the same thing as you would have if you had simply multiplied the number by 3 and added 11 to that result. 3. If you have 17 identical objects in a box and you add 4 more of the same exact object type to the box, then the box will now contain 21 of those objects.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:VERBAL IF-THEN'S
For each of the following, do your best to figure out if the statement is true or false. Give an explanation (or
argument) justifying why you think what you think.
NOTE: Each of the following refers to "a number" or “numbers". They are general statements. So, if there is any
number (or numbers) for which it's false, then the statement is false. In other words, if you are thinking "that's
true in some cases (or perhaps even many cases), but it's not true in all cases," then the statement is false.
Warning: The word "number" does not mean "integer" or "positive integer". All integers are numbers, but not
all numbers are integers. Integers are numbers like -13, -4, 0, 27, and 132. Non-integers are numbers like 2.61,
- 5.8, and 55/9. The first of these is between the consecutive integers 2 and 3. The second is between
-6 and -5. The third is between 6 and 7. So if you are going to test the statements by choosing a number or
numbers to test it with, do not limit yourself to the simplest case, which is positive integers only. Many things
are true for positive integers that are not true in general.
1. If you add two numbers together and square the result, then you'll get the same thing as squaring the two
numbers and adding those two results. (Note: "Squaring" something means to multiply it by itself. For
example, squaring 8 yields 8x8 = 64 .)
2. If you multiply a number by 6, add 11 to that result, and divide that result by 2, then you'll get the same
thing as you would have if you had simply multiplied the number by 3 and added 11 to that result.
3. If you have 17 identical objects in a box and you add 4 more of the same exact object type to the box, then
the box will now contain 21 of those objects.
4. If you add 13 to a number and subtract 13 from that result, then you'll end up with the original number.
5. If you multiply a number by itself and take the square root of the result, then you'll end up with the original
number.
6. If you multiply a non-zero number by 12, then the result will not have the same value as the original
number.
7. Ifyou add two number and take the absolute value of the result, then you'll get the same thing as taking the
absolute value of the two numbers and adding those two results. (Note: The absolute value of a number is
it's distance from 0.)
8. If one number (the first one) is less than another (the second one) and you multiply each of them by some
third number, then the first times the third will be less than the second times the third.
9. If you add two numbers and triple the result, then you'll get the same thing as tripling the two numbers and
adding those two results.
10. If you square a number, then the result will always be greater than or perhaps equal to the original number.
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