Question : 8

For any two integers $x a n d y$ , which of the following suggests that operation of addition is commutative ?

(a) $x + y = y + x$

(b) $x + y > x$

(c) $x - y = y - x$

(d) $x y = y x$

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Solution

Option (a).

Commuting the order of numbers in addition does not change the sum.

Commutative property of addition for two numbers $x a n d y$ can be written as $x + y = y + x$ .

For example, 3+4 = 4+3 = 7.

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Question : 8

For any two integers $x a n d y$ , which of the following suggests that operation of addition is commutative ?

(a) $x + y = y + x$

(b) $x + y > x$

(d) $x y = y x$

X & Y; X \cup Y = Y \cup X .

(i) x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2}) (i i) x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

Question 100 (i)

Express the following property with variables x, y and z.

Commutative property of addition

t a n \frac{1}{2} [s i n^{- 1} \frac{2 x}{1 + x^{2}} + c o s^{- 1} \frac{1 - y^{2}}{1 + y^{2}}]

| x | < 1, y > 0 a n d x y < 1

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