Statement 1: For a whole number x, x - 0 = x implies 0 is identity element for subtraction.
Statement 2: For a whole number x, 0 - x = x implies 0 is identity element for subtraction.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1: x - 0 = x shows that 0 is a right identity for subtraction. But 0 is an identity element only if it works from both the right and the left, i.e. 0 - x = x must also hold. Since 0 - x ≠ x, the number 0 is not the identity element for subtraction.
∴ Statement 1 is false.
Statement 2: 0 - x = x is not true for whole numbers (for example, 0 - 5 = -5 ≠ 5), so 0 is not the identity element for subtraction.
∴ Statement 2 is false.
Hence, option 2 is the correct option.
Statement 1: On subtracting a whole number from another whole number, the result is a natural number.
Statement 2: 15 and 25 are whole numbers, but 15 - 25 is not a natural number.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Answer
Statement 1: Subtracting one whole number from another does not always give a natural number. For example, 5 - 5 = 0 (which is not a natural number) and 5 - 8 = -3 (which is not even a whole number).
∴ Statement 1 is false.
Statement 2: 15 - 25 = -10, which is a negative number and hence not a natural number. So the statement is correct.
∴ Statement 2 is true.
Hence, option 4 is the correct option.