MATHS TRUE / FALSE

The product of two integers is always greater than the sum of the integers. (False)
Correct :
Let two integers be -2 and 3
Then product = -2 × 3 = -6
and sum = -2 + 3 = 1
But -6 < 1
Their product < Their sum.

For any two integers a and b, the inequality -a < b is always true. (False)
Correct : Let a = -5 and b = 2, then -a = -(-5) = 5 and -a > b

The sum of two integers is always greater than their difference. (False)
Correct : As 3 + (-4) = -1 but 3 – (-4) = 3 + 4 = 7 and -1 < 7

The sum of a positive integer and a negative integer is always a positive integer. (False)
Correct : As 3 + (-8) = 3 – 8 = -5 which is negative.

The successor of 0 × (-10) is 1 × (-10). (False)
Correct : As 0 × (-10) = 0 and successor of 0 is 1 but 1 × (-10) = -10

For every integer a, a ÷ a = 1. (False)
Correct :
As 0 ÷ 0 ≠ 1

[(-32 ÷ 8] ÷ 2 = (-32) ÷ (8 ÷ 2) (False)
Correct :
[(-32) ÷ 8} ÷ 2 = -4 ÷ 2 = -2
and (-32) ÷ (8 ÷ 2) = -32 ÷ 4 = -8
So, it is false.

Multiplication fact (-8) × (-12) = 96 is same as division fact 96 ÷ (-12) = -8. (True)

(-1) is not a mutliplicative identity of integers. (True)

Commutative property does not hold for division of integers. (True)

Associative property holds for subtraction of integers. (False)
Correct :
It does not holds as
= 15 – 7 = 8
= 7 – 15 = -8
So, 8 ≠ (-8)

Commutative property does not hold for subtraction of integers. (True)

Closure property holds for subtraction of integers. (True)

The product of 5 negative integers is a negative integer. (True)

(-237) × 0 is same as 0 × (-89). (True)

(-5) × (-8) × 0 is a positive integer. (False)
Correct : (-5) × (-8) × 0 which is neither positive nor-negative.

(-17) × 6 is a whole number. (False)
Correct : (-17) × 6 = -102 is not a whole number as a whole numebr is zero or positive.

1 is the additive identity of integers. (False)
Correct : 0 is a additive identity not 1.

If we divide an integer by (-1), then the result is the additive inverse of the integer. (True)

If we multiply an integer by (-1), then the result is the additive inverse of the integer. (True)

Going 300 metres towards east first and then 100 m back is the same as going 100 m towards west first and then going 300 back. (True)

We can write a pair of integers whose sum is not an integer. (False)
Correct : As sum of two integers is always an integer.

The difference of two negative integers cannot be a positive integer. (False)
Correct : Difference of -3 and -5 = -3 – (-5) = -3 + 5 = 2 which is positive

For every integer a, |a| is either positive or zero. (True)