Question 59.

Match Column I with Column II.

$\begin{matrix} C o l u m n I & C o l u m n I I (i) & T h e a d d i t i v e i n v e r s e o f + 2 & (a) & 0 (i i) & T h e g r e a t e s t n e g a t i v e i n t e g e r & (b) & - 2 (i i i) & T h e g r e a t e s t n e g a t i v e e v e n i n t e g e r & (c) & 2 (i v) & T h e s m a l l e s t i n t e g e r g r e a t e r t h a n e v e r y n e g a t i v e i n t e g e r & (d) & 1 (v) & S u m o f p r e d e c e s s o r a n d s u c c e s s o r o f - 1 & (e) & - 1 \end{matrix}$

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Solution

(i) The additive inverse of a number x is the number that when added to x yields zero. It is obtained by reversing the sign of the number. The additive inverse of 2 is -2.

(ii) The greatest negative integer is -1.

(iii) The greatest negative even integer is -2.

(iv) The smallest integer greater than every negative integer is 0.

(v) Sum of predecessor and successor of -1 is -2.

The predecessor of a number is obtained by subtracting one from the number.

The successor of a number is obtained by adding one to the number.

The predecessor of -1 = -1 - 1 = -2

The successor of -1 = -1 + 1 = 0

Now, sum of -2 and 0 = -2 + 0 = -2

Hence, the correct matching is

(i) $\to$ b (ii) $\to$ e (iii) $\to$ b

(iv) $\to$ a (v) $\to$ b

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Question 59.

Match Column I with Column II.

$\begin{matrix} Column I & Column II (i) & The additive inverse of +2 & (a) & 0 (ii) & The greatest negative integer & (b) & - 2 (iii) & The greatest negative even integer & (c) & 2 (iv) & The smallest integer greater than every negative integer & (d) & 1 (v) & Sum of predecessor and successor of -1 & (e) & - 1 \end{matrix}$

Q. Which of the following statements are true:

(i) −13 > −8 − (−2)
(ii) −4 + (−2) < 2.
(iii) The negative of a negative integer is positive.
(iv) If a and b are two integers such that a > b, then a − b is always positive integer,
(v) The difference of two integers is an integer.
(vi) Additive inverse of a negative integer is negative.
(vii) Additive inverse of a positive integer is negative.
(viii) Additive inverse of a negative is positive.

Question 13

The additive inverse of a negative integer

(a) is always negative

(b) is always positve

(d) zero

Q. For each of the following statements, write (T) for true and (F) for false:

(i) The smallest integer is zero.
(ii) − 10 is greater than − 7
(iii) Zero is larger than every negative integer.
(iv) The sum of two negative integers is a negative integer.
(v) The sum of a negative integer and a positive integer is always a positive integer.

Q. Which of the following statements are true?

(i) The smallest integer is zero.

(ii) The opposite of zero is zero.

(iii) Zero is not an integer.

(iv) 0 is larger than every negative integer.

(v) The absolute value of an integer is greater than the integer.

(vi) A positive integer is greater than its opposite.

(vii) Every negative integer is less than every natural number.

(viii) 0 is the smallest positive integer.

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Question 59. Match Column I with Column II. Column IColumn II(i)The additive inverse of +2(a)0(ii)The greatest negative integer(b)−2(iii)The greatest negative even integer(c)2(iv)The smallest integer greater than every negative integer(d)1(v)Sum of predecessor and successor of −1(e)−1