Question

Which of the following statement is true?

a) Every positive integer is larger than every negative integer.
b) Zero is greater than every positive integer.
c) Zero is smaller than every negative integer.
d) Farther a number from zero to the right , smaller is its value.​

Answer 1

Step-by-step explanation:

a) We know that on a number line the number on the right is always greater than the number on the left. Same applies for integers also.  -1 > -2, -2 > -3 and so on.

0 is on the left of all the positive integers. So, 0 is less than every positive integer. 0 is on the right of all the negative integers. So, 0 is greater than every negative integer. All the positive integers are greater than negative integers.

b) 0 is on the left of all the positive integers. So, 0 is less than every positive integer. 0 is on the right of all the negative integers. So, 0 is greater than every negative integer.

c) Zero is neither positive or negative. It's bigger than any negative number, but smaller than every positive number.

d) Negative numbers are smaller than zero. Negative numbers get smaller and smaller the farther they are from zero. This can get confusing because you may think that –400 is bigger than –12. But just think of –400° F and –12° F. Neither temperature is pleasant to think about, but –400° is definitely less pleasant — colder, lower, smaller. When dealing with negative numbers, the number closer to zero is the bigger number.

Answer 2

The statement which is true among the given options is (a) Every positive integer is larger than every negative integer.

Step-by-step explanation:  

• We know, positive integers are those greater than 0 and negative integers are those smaller than 0. Hence, every positive integer is greater that every negative integer. For example: $1>-7, 6>-6, 9>-2 etc.$ Hence, Option (a) is True.

• We know, 0 can never be greater than a positive integer. For Example:$0<8, 0<1, 0< 10000.$ It will be always lesser than a positive integer. Hence, Option (b) is False

• We know, 0 is always greater than a negative integer. For example: $0>-1, 0>-6, 0>-10000.$ Hence, Option (c) is False.

• We also know that the right side of the number line consists of positive integers and the left side consists of negative integer. As a number goes farther from 0 to the right side, its values keep on increasing. For example:$0<2,0<90, 0<10000008.$ Hence, Option (d) is also False.

Hence, The statement which is true among the given options is (a) Every positive integer is larger than every negative integer.