# symbols as operations

• May 29th 2012, 05:08 PM
klg
symbols as operations
the question is as follows:
For all numbers x and y, let the operation ■ be defined by x ■ y = xy-y. If a and b are positive integers, which of the following can be equal to zero?

I. a■b
II. (a+b)■b
III. a■(a+b)

does one distribute choices II and III to a■b + b■b and a■a + a■b respectively? How does that help?
There is just something about the use of symbols that has not registered yet. Thanks.
• May 29th 2012, 06:13 PM
Plato
Re: symbols as operations
Quote:

Originally Posted by klg
the question is as follows:
For all numbers x and y, let the operation ■ be defined by x ■ y = xy-y. If a and b are positive integers, which of the following can be equal to zero?
I. a■b
II. (a+b)■b
III. a■(a+b)

$I~a \bullet b = ab - b$

$II~(a + b) \bullet b = (a + b)b - b$

$III~a \bullet (a + b) = a(a + b) - (a + b)$
• May 29th 2012, 06:15 PM
emakarov
Re: symbols as operations
Quote:

Originally Posted by klg
does one distribute choices II and III to a■b + b■b and a■a + a■b respectively?

Let's see. By definition, (x + y) ■ z = (x + y)z - z = xz + yz - z, while x ■ z + y ■ z = xz - z + yz - z = xz + yz - 2z. So, ■ does not distribute over + on positive integers.

A binary operator is just a function of two arguments. Expand ■ according to its definition in each expression so that you only have plus and times left.
• May 29th 2012, 06:45 PM
klg
Re: symbols as operations
Thank you very much! Now this makes sense, I just hope I can apply this the next time.
The text passage contains a mathematical question involving a custom operation and asks which of the given expressions can be equal to zero. An answer is not provided in the text, only the problem statement and some guidance on how to approach the problem.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# symbols as operations

• May 29th 2012, 05:08 PM
klg
symbols as operations
the question is as follows:
For all numbers x and y, let the operation ■ be defined by x ■ y = xy-y. If a and b are positive integers, which of the following can be equal to zero?

I. a■b
II. (a+b)■b
III. a■(a+b)

does one distribute choices II and III to a■b + b■b and a■a + a■b respectively? How does that help?
There is just something about the use of symbols that has not registered yet. Thanks.
• May 29th 2012, 06:13 PM
Plato
Re: symbols as operations
Quote:

Originally Posted by klg
the question is as follows:
For all numbers x and y, let the operation ■ be defined by x ■ y = xy-y. If a and b are positive integers, which of the following can be equal to zero?
I. a■b
II. (a+b)■b
III. a■(a+b)

$I~a \bullet b = ab - b$

$II~(a + b) \bullet b = (a + b)b - b$

$III~a \bullet (a + b) = a(a + b) - (a + b)$
• May 29th 2012, 06:15 PM
emakarov
Re: symbols as operations
Quote:

Originally Posted by klg
does one distribute choices II and III to a■b + b■b and a■a + a■b respectively?

Let's see. By definition, (x + y) ■ z = (x + y)z - z = xz + yz - z, while x ■ z + y ■ z = xz - z + yz - z = xz + yz - 2z. So, ■ does not distribute over + on positive integers.

A binary operator is just a function of two arguments. Expand ■ according to its definition in each expression so that you only have plus and times left.
• May 29th 2012, 06:45 PM
klg
Re: symbols as operations
Thank you very much! Now this makes sense, I just hope I can apply this the next time.
user
The text passage contains a mathematical question involving a custom operation and asks which of the given expressions can be equal to zero. An answer is not provided in the text, only the problem statement and some guidance on how to approach the problem.

TYPE: SINGLE_QUESTION