Integers — Statement I-II Type Questions

Statement 1 : The additive inverse of (-a) is a.

Statement 2 : Multiplicative inverse of an integer a is $\dfrac{1}{a}$.

Which of the following options is correct ?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Statement 1 : For any integer, the sum of the integer and its additive inverse is 0. Since (-a) + a = 0, the additive inverse of (-a) is a. Hence, Statement 1 is true.

Statement 2 : The multiplicative inverse exists only for non-zero integers, not for any integer (it does not exist for a = 0). Hence, Statement 2 is false.

Hence, option 3 is the correct option.

Statement 1 : 16 ÷ (8 ÷ 4) = (16 ÷ 8) ÷ 4

Statement 2 : Subtraction of integers is not associative.

Which of the following options is correct ?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Statement 1 : L.H.S. = 16 ÷ (8 ÷ 4) = 16 ÷ 2 = 8 and R.H.S. = (16 ÷ 8) ÷ 4 = 2 ÷ 4 = $\dfrac{1}{2}$.

Since 8 ≠ $\dfrac{1}{2}$, Statement 1 is false.

Statement 2 : Subtraction of integers is not associative, i.e. a - (b - c) ≠ (a - b) - c in general. Hence, Statement 2 is true.

Hence, option 4 is the correct option.