Question

# State whether the following statements are true or false. Give reasons for your answer. (i) Every natural number is a whole number. (ii) Every whole number is a natural number. (iii) Every integer is a whole number. (iv) Every integer is a rational number. (v) Every rational number is an integer. (vi) Every rational number is a whole number.

Solution

## (i) Every natural number is a whole number. Natural number: (All numbers starting from 1) 1,2,3,4,5,.... Whole numbers: (All numbers starting from 0 ) 0,1,2,3,4,5,.... 1,2,3,4,5,.... are both natural as well as whole numbers. thus, All natural numbers are the whole numbers.   so, True (ii)Every whole number is a natural number. Natural number: (All numbers starting from 1) 1,2,3,4,5,.... Whole numbers: (All numbers starting from 0 ) 0,1,2,3,4,5,.... Here, we can see Zero is a whole number but not a natural number. so, It is False (iii) Every integer is a whole number. Integers: (All numbers both negative and positive) .......,-3,-2,-1,0,1,2,3,.... Whole numbers: (All numbers starting from 0 ) 0,1,2,3,4,5,.... As integers may be negative but whole numbers are positive. Eg: -3 is an integer but not whole number so, False (iv) Every integer is a rational number. Integers: (All numbers both negative and positive) .......,-3,-2,-1,0,1,2,3,.... Rational number: (All numbers in the form of  ) where both p and q are integers, . Eg: -3,-2,-1,0,1,2,3 are both Integers as well as rational numbers, thus, Every integer is a rational number. so, True (v) Every rational number is an integer. Rational number: (All numbers in the form of  ) where both p and q are integer , . Eg: Integers: (All numbers both negative and positive) .......,-3,-2,-1,0,1,2,3,.... here,  Fraction like are Rational Number but not Integers. So,  Statement is False (vi) Every rational number is a whole number. Rational number: (All numbers in the form of  ) where both p and q are integer , . Eg: Whole numbers: (All numbers starting from 0 ) 0,1,2,3,4,5,.... Fractions like     MathematicsSecondary School Mathematics IXStandard IX

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