Q. 14.0( 5 Votes )

# Fill in the blank

Answer :

(a) The number 0 is not in the set of **natural numbers.**

0 is added to set of natural number (1,2,3,4,…..) and it becomes set of whole numbers (0,1,2,3,4,….)

(b) The least number in the set of all the whole numbers is **0.**

0 is the smallest number which when added to the set of natural number make it a set of whole number.

(c) The least number in the set of all even natural numbers is __2.__

The set of even natural number starts from (2,4,6,….) so the least number in the set of all even natural numbers is number 2 .

(d) The successor of 8 in the set of all natural numbers is **9.**

The number succeeding number 8 is number 9 in the set of all natural numbers as the set of natural number consist of term (1,2,3,4,5,6,7,8,9,10,11,12,…..)

(e) The sum of two odd integers is **always an even number**

for e.g;- 3 + 5 = 8 , 5 + 7 = 12

Let m and n be odd integers. By definition of odd we have that m = 2a + 1 and

n = 2b + 1. Consider the sum m + n = (2a + 1) + (2b + 1) = 2ab + 2b + 2 = 2k, where

k = a + b + 1 is an integer. Therefore by definition of even we have shown that

m + n is even.

(f) The product of two odd integers is **odd.**

Let a and b be two odd integers.

By definition of odd we know that a = 2m + 1 and b = 2n + 1.

Now, the product ab = (2m + 1)(2n + 1)

= 4mn + 2m + 2n + 1

= 2(2mn + m + n) + 1 = 2k + 1, where k = (2mn + m + n ) is an integer. Therefore by

Definition of odd number, the product of two odd integers is also odd.

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