Question

Which of the following statements are true and which are false?
(i) The sum of two integers is always an integer.
(ii) The difference of two integers is always an integer.
(iii) −14 > −8 − (−7)
(iv) −5 − 2 > −8
(v) (−7) − 3 = (−3) − (−7)

Answer 1

(i) True
An integer added to an integer gives an integer.

(ii) True
An integer subtracted from an integer gives an integer.

iii) False
−8 − (−7)
= −8 + 7
= −1
Since 14 is greater than 1, −1 is greater than −14.

iv) True
−5 − 2 = −7
Since 8 is greater than 7, −7 is greater than −8.
− 7 > −8

​v) False
L.H.S.
(−7) − 3 = −10
R.H.S.
(−3) − (−7)
= (−3) + 7
= 4
$\therefore$ L.H.S. $\ne$ R.H.S.