a.
To write: whether set of positive integers are closed under
a.
Answer to Problem 40WE
No, positive integers are not closed under
Explanation of Solution
Given information: A set of numbers is said to be closed under an operation if the result of combining any two numbers in the set results in a number that is also in the set
Take
Here,
Now find
But
So, positive integers are not closed under
b.
To write: whether set of odd integers are closed under
b.
Answer to Problem 40WE
Yes, set of odd integers are closed under
Explanation of Solution
Every odd integer is of the form
Let
Now find
Let
So,
So,
c.
To write: whether set of odd integers are closed under
c.
Answer to Problem 40WE
No, set of odd integers are not closed under
Explanation of Solution
Take
Here,
Now find
But
(
So, odd integers are not closed under
d.
To write: whether set of integers ending in 4 or 6 are closed under
d.
Answer to Problem 40WE
Yes, set of integers ending in 4 or 6 are closed under
Explanation of Solution
Let
Then
For example:
Take
So,
Therefore, set of integers ending in 4 or 6 are closed under
Chapter 2 Solutions
Algebra: Structure And Method, Book 1
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