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Combination of n Different Things Taken One or More at a Time

Does every ne...

Question

Does every negative integer have a corresponding positive integer?

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Solution

Yes, every negative integer has a corresponding positive integer, for example, $- 1$ has a corresponding positive integer $1$ , $- 2$ has a corresponding positive integer $2$ , $- 3$ has a corresponding positive integer $3$ , and so on.

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Q. For each of the following statements, write (T) for true and (F) for false:

(i) The smallest integer is zero.
(ii) − 10 is greater than − 7
(iii) Zero is larger than every negative integer.
(iv) The sum of two negative integers is a negative integer.
(v) The sum of a negative integer and a positive integer is always a positive integer.

Q. Which of the following statements are true and which are false?

(i) The product of a positive and a negative integer is negative.
(ii) The product of two negative integers is a negative integer.
(iii) The product of three negative integers is a negative integer.
(iv) Every integer when multiplied with −1 gives its multiplicative inverse.
(v) Multiplication on integers is commutative.
(vi) Multiplication on integers is associative.
(vii) Every nonzero integer has a multiplicative inverse as an integer.

Q. Which of the following statements are true?

(i) The smallest integer is zero.

(ii) The opposite of zero is zero.

(iii) Zero is not an integer.

(iv) 0 is larger than every negative integer.

(v) The absolute value of an integer is greater than the integer.

(vi) A positive integer is greater than its opposite.

(vii) Every negative integer is less than every natural number.

(viii) 0 is the smallest positive integer.

Q. Which of the following statements are true and which are fals?
(i) The product of a positive integer and a negative integer is negative.
(ii) The product of two negative integers is a negative integer.
(iii) The product of three negative integers is a negative integer.
(iv) Every integer when multiplied with −1 gives its multiplicative inverse.

Question 22.

State True/False

Every positive integer is larger than every negative integer.

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Combination of n Different Things Taken One or More at a Time

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