Question

A+(b+c)=(a+b)+c what property is this? The options are as follows

Identity property of multiplication
Associative property of multiplication
Identity prop. Of addition
Multiplicative inverse prop.
Additive inverse prop.
Commutative prop of addition
Commutative prop of multiplication
Transitive property
Properties

Answer 1

Given:

The properties and their notations are given.

To match:

Step-by-step explanation:

31. It is given that,

`a+0=a`

Since zero is the additive identity.

So, the property is an identity property of addition.

32. It is given that,

`a+b=b+a`

Here, the property is the commutative property of addition.

33. It is given that,

`a\cdot(b\cdot c)=(a\cdot b)\cdot c`

Here, the property is an Associative property of multiplication.

34. It is given that,

`a+(-a)=0`

Since -a is the additive inverse of a.

So, the property is the Inverse property of addition.

35. It is given that,

`a\cdot1=a`

Since 1 is the multiplicative identity.

So, the property is an identity property of multiplication.

36. It is given that,

`a\cdot(b+c)=ab+ac`

Here, the property is a distributive property of addition.

37. It is given that,

`a\cdot b=b\cdot a`

Here, the property is a commutative property of multiplication.

38. It is given that,

`a\cdot(1)/(a)=1`

Here, the property is an inverse property of multiplication.

39. It is given that,

`a+(b+c)=(a+b)+c`

Here, the property is an Associative property of addition.

Final answer:

31. E

32. A

33. D

34. AC

35. AB

36.