Question

State whether the following statements are true or false. If the statement is false, give
an example.
1.Closure property holds for subtraction of natural numbers.........
2. Associative property holds for division of integers...........
3.Commutative property holds for addition of natural numbers.............
4.Commutative property does not hold for subtraction of rational numbers..........
5. If a property holds for rational............. numbers then it holds for integers as well.........
6. Reciprocal of every rational number is a rational number..........
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Answer 1

State whether the following statements are true or false. If the statement is false, give  an example.

1. Closure property holds for subtraction of natural numbers.........

► False

Closure property does not hold, if any of the number in case of multiplication and division, is not a natural number

Example –

-2 x 3 = -6; Not a natural number

6/-2 = –3 but –3 isn't a natural number

2. Associative property holds for division of integers...........

► False

Associative property does not holds for division and subtraction  of integers.

Example –

Subtraction : a – ( b – c ) ≠ ( a – b ) – c => 2 – (15 – 1 ) = – 12 and ( 2 – 15 ) – 1 = – 14.

3. Commutative property holds for addition of natural numbers.............

► True

4. Commutative property does not hold for subtraction of rational numbers..........

► True

5. If a property holds for rational............. numbers then it holds for integers as well.........

► False

6. Reciprocal of every rational number is a rational number..........

► True

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