Question

Consider the set A= {1,3,5,7,9,…} i.e. a set of odd positive integers. Determine whether A is

closed under i) multiplication ii) addition .​

Answer 1

Answer:

The set B of odd numbers between 1 and 10 exclusive. 5) The set A of solutions to the problem: x + 6 = 10. 6) The set A of solutions to the problem x – 4 = 9. 7) The set B of flavors of ice ...

Step-by-step explanation:

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Answer 2

• A is closed under multiplication

• A is not closed under addition

Given :

The set A = { 1 , 3 , 5 , 7 , 9 , . . . . } i.e. a set of odd positive integers

To find :

Determine whether A is closed under i) multiplication ii) addition

Concept :

A set S is said to be closed under an operation * if for all a , b ∈ A we have a*b ∈ A

Solution :

Step 1 of 3 :

Write down the given set

Here the given set is A = { 1 , 3 , 5 , 7 , 9 , . . . . } i.e. a set of odd positive integers

Step 2 of 3 :

Check whether A is closed under multiplication

A = { 1 , 3 , 5 , 7 , 9 , . . . . }

For all a , b ∈ A we have a × b ∈ A

Hence A is closed under multiplication

Step 3 of 3 :

Check whether A is closed under addition

A = { 1 , 3 , 5 , 7 , 9 , . . . . }

1 , 3 ∈ A

But 1 + 3 = 4 ∉ A

For all a , b ∈ A we have a + b ∉ A

Hence A is not closed under addition

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