Question

1.Which property justifies the statement if y=7 then 7=y?

A. reflexive property
B. identity property
C. symmetric property
D. transitive property
2.Which set of number is closed under subtraction
A. Natural number
B. Integer
C. Irrational number
D. odd numbers
3. Which property justifies the statement (a-b)*0=0
A. Inverse property
B. Associative property
C. Distributive property
D. zero product property

Answer 1

1. option C, i.e., symmetric property.

2. option B, i.e., Integer

3. option D, i.e., zero product property

Explanation:

Symmetric property: According to this property it a=b the b=a.

By symmetric property, we can say that, if y=7 then 7=y.

Therefore, the correct option is C, i.e., symmetric property.

Closure property: According to this property, if a∈S and b∈S, then a*b∈S.

Subtraction of natural numbers is not always natural.

`1\in N,2\in 2, 1-2=-1\\otin N`

Subtraction of integers is always integer.

Subtraction of irrational number is not always irrational number.

`\sqrt 2\in Q, \sqrt 2-\sqrt 2=0\\otin Q`

Subtraction of odd number is always even.

Therefore, the correct option is B, i.e., Integer.

Given statement is (a-b)*0=0.

According to zero product property if ab=0, then a=0 or b=0.

So, the given statement is true by zero product property.

Therefore, the correct option is D, i.e., zero product property.