State whether true or false. Do working and give examples to prove your point.
1. Sum of any integers is always greater than
their difference
2. (-28 +46) + 46+ (-28)
3. Additive inverse of -119 is 119.
4. On adding any integer with its additive
inverse, we get the additive identity.
Write a pair of integers for which the following statements are true.
1. Sum is zero.
2. Difference is zero.
3. Additive inverse of -119 is 119.
4. On adding any integer with its additive
inverse, we get the additive identity.
5. Sum is a negative number.
6. Difference is a negative number.
Answers
Answer:
(1) False
(2) True
(3) True
(4) True
(5) False
(6) False
Step-by-step explanation:
(1)
Sum of any integers is always greater than
their difference
Solution:
Since
-3 + (-2) = -5
But
-3 - (-2) = -3 + 2 = -1
And -1 > -5
In above special case difference is greater then sum so
Statement (1) is false.
(2)
(-28 + 46) = 46 + (-28)
Solution:
Since
(-28 + 46) = 18
And
46 + (-28) = 18
This implies
Statement (2) is right
(3)
Additive inverse of -119 is 119
Solution:
Since
-119 + 119 = 0 = additive identity
This implies
Additive inverse of -119 is 119
So
Statement (3) is right.
(4)
On adding any integer with its additive
inverse, we get the additive identity.
Solution:
Let x be integer then -x will its additive inverse
And note
x + (-x) = (-x) + x = 0 = additive identity
This implies
Statement (4) is true.
(5)
Sum is a negative number.
Solution:
Sum of 2 and 3 is 5 which is positive integer
Sum of -2 and 3 is 1 which is positive integer
Sum of -9 and 3 is -6 which is negative integer
You see some times sum is positive and some times sum is negative.
So
Statement (5) is false in general.
(6)
Difference is a negative number.
Solution:
Difference of 2 and 3 is -1 which is negative integer
Difference of -2 and 3 is -5 which is negative integer
Difference of 9 and 3 is 6 which is positive integer
You see some times Difference is positive and some times Difference is negative.
So
Statement (6) is false in general.