State whether the following statements are True (T) or False (F):
(i) For every integer a, |a| is either positive or zero.
(ii) The difference of two negative integers cannot be a positive integer.
(iii) We can write a pair of integers whose sum is not an integer.
(iv) 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.
(v) If we multiply an integer by (-1), then the result is the additive inverse of the integer.
(vi) If we divide an integer by (-1), then the result is the additive inverse of the integer.
(vii) 1 is the additive identity of integers.
(viii) (-17) × 6 is a whole number.
(ix) (-5) × (-8) × o is a positive integer.
(x) (-237) × 0 is same as 0 × (-89).
(xi) The product of 5 negative integers is a negative integer.
(xii) Closure property holds for subtraction of integers.
(xiii) Commutative property does not hold for subtraction of integers.
(xiv) Associative property holds for subtraction of integers.
(xv) Closure property holds for division of integers.
(xvi) Commutative property does not hold for division of integers.
(xvii) (-1) is not a mutliplicative identity of integers.
(xviii) Multiplication fact (-8) × (-12) = 96 is same as division fact 96 ÷ (-12) = -8.
(xix) [(-32 ÷ 8] ÷ 2 = (-32) ÷ (8 ÷ 2)
(xx) For every integer a, a ÷ a = 1.
(xxi) The successor of 0 × (-10) is 1 × (-10).
Solution:
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