Question

For each of the following statements, write (T) for true and (F) for false:
(i) The smallest integer is zero.
(ii) Zero is not an integer.
(iii) The opposite of zero is zero.
(iv) −10 is greater than −6.
(v) The absolute value of an integer is always greater than the integer.
(vi) 0 is larger than every negative integer.
(vii) Every negative integer is less than every natural number.
(viii) The successor of −187 is −188.
(ix) The predecessor of −215 is −214.

Answer 1

i) False
This is because 0 is greater than every negative integer.

ii) False
0 is an integer as we know that every whole number is an integer and 0 is a whole number.

iii) True
0 is an integer that is neither positive nor negative. So, the opposite of zero is zero.

iv) False
Since 10 is greater than 6, -10 is smaller than -6.

v) True
This is because an absolute value is a positive number. For example, -2 is an integer, but its absolute value is 2 and it is greater than -2.

vi) True
This is because all negative integers are to the left of 0.

vii) True
This is because natural numbers are positive and every positive integer is greater than every negative integer.

viii) False
This is because the successor of -187 is equal to -186 (-186 + 1). In succession, we move from the left to the right along a number line.

ix) False
This is because the predecessor of -215 is -216 (-216 - 1). To find the predecessor, we move from the right to the left along a number line.