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Patterns in Whole Numbers

Write the con...

Question

Write the converse of the following statement : ' If two integers a and b are such that a > b, then a - b is always a positive integer'.

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Solution

The converse of the given statement is:

If two integers a and b are such that a - b is always a positive integer, then a > b.

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Similar questions

p, q

are statements expressed as

p :

If two integers

a

b

a > b

a - b

is always a positive integer

q :

If two integers

a

b

a - b

is always a positive integer, then

a > b,

then which among the following is correct regarding statements

p

q

Q. Which of the following statements are true:

(i) −13 > −8 − (−2)
(ii) −4 + (−2) < 2.
(iii) The negative of a negative integer is positive.
(iv) If a and b are two integers such that a > b, then a − b is always positive integer,
(v) The difference of two integers is an integer.
(vi) Additive inverse of a negative integer is negative.
(vii) Additive inverse of a positive integer is negative.
(viii) Additive inverse of a negative is positive.

Write the converse and contrapositive of each of the following statements:

(i) If n is an even number, then $n^{2}$ is even.

(ii) If two integers a and b are such that $a > b,$ then $(a - b)$ is always a positive integer.

(iii) If a $Δ A B C$ is right angled at B, then $A B^{2} + B C^{2} = A C^{2} .$

(iv) If $Δ A B C$ and $Δ D E F$ are congruent, then they are equiangular.

(v) You cannot comprehend geometry if you do not know how to reason deductively.

(vi) Something is cold implies that it has low temperature.

Q. Which of the following statements are true?
(i) The product of a positive and a negative integer is negative.
(ii) The product of three negative integers is a negative integer.
(iii) Of the two integers, if one is negative, then their product must be positive.
(iv) For all non-zero integers a and b, a × b is always greater than either a or b.
(v) The product of a negative and a positive integer may be zero.
(vi) There does not exist an integer b such that for a> 1, a × b = b × a = b.

a, b, c

be positive integer such that

\frac{a \sqrt{2} + b}{b \sqrt{2} + c}

is a rational number, then which of the following is always an integer?

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