If x-49-y-712 and z-23- then verify that x-y-z-x-y-z-

x=49, y= 712, z= 23 then #160; x (y 2)≠(x y) z ⇒49 [ 712 ( 23)]≠[49 ( 712)] ( 23) ⇒49 [ 712+23]≠[49+712] ( 23) ⇒49 [ 7+812]≠[16+2136] ...

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Standard XII

Mathematics

Logical Connectives

If x=49,y=-...

Question

If $x = \frac{4}{9}, y = \frac{- 7}{12}$ and $z = \frac{- 2}{3}$ , then verify that $x - (y - z) \neq (x - y) - z$ .

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Solution

$x = \frac{4}{9}, y = \frac{- 7}{12}, z = \frac{- 2}{3}$ then
$x - (y - 2) \neq (x - y) - z$
$\Rightarrow \frac{4}{9} - [\frac{- 7}{12} - (\frac{- 2}{3})] \neq [\frac{4}{9} - (\frac{- 7}{12})] - (\frac{- 2}{3})$
$\Rightarrow \frac{4}{9} - [\frac{- 7}{12} + \frac{2}{3}] \neq [\frac{4}{9} + \frac{7}{12}] - (\frac{- 2}{3})$
$\Rightarrow \frac{4}{9} - [\frac{- 7 + 8}{12}] \neq [\frac{16 + 21}{36}] + \frac{2}{3}$
$\Rightarrow \frac{4}{9} - \frac{1}{12} \neq \frac{37}{36} + \frac{2}{3}$
$\Rightarrow \frac{16 - 3}{36} \neq \frac{37 + 24}{36}$
$\frac{13}{36} \neq \frac{61}{36}$ proved
$L . H . S$ and $R . H . S$ are not equal

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Similar questions

Verify the property: $x \times (y \times z) = (x \times y) \times z b y t a k i n g :$

(i) $x = \frac{- 7}{3}, y = \frac{12}{5}, z = \frac{4}{9}$

(ii) $x = 0, y = \frac{- 3}{5}, z = \frac{- 9}{4}$

(iii) $x = \frac{1}{2}, y = \frac{5}{- 4}, z = \frac{- 7}{5}$

(iv) $x = \frac{5}{7}, y = \frac{- 12}{13}, z = \frac{- 7}{18}$

$Verify that x \times (x - z) = x \times y - x \times z, i f (i) x = \frac{4}{5}, y = - \frac{7}{4} ~ a n d z = 3 (i i) x = \frac{3}{4}, y = \frac{8}{9} ~ a n d z = - 5$

Q. If

x = \frac{4}{7}, y = \frac{1}{2}

and

z = (- \frac{3}{4})

, then verify the following:
(i)

x \div y \neq y \div x

(ii)

(x \div y) \div z \neq x \div (y \div z)

(iii)

x \div (y + z) \neq x \div y + x \div z

(iv)

x \div (y - z) \neq x \div y - x \div z

Q. For the following values of x, y and z. Verify the distributive property of rational numbers: [4 MARKS]

x \times (y + z) = x \times y + x \times z

x = - 3, y = \frac{9}{2}, z = \frac{- 7}{9}

If x, y and z are variables, verify the cyclic symmetry of the following expressions.

(1) x(y + z) + y(z + x) + z(x + y)

(2) xy(x − y) + yz(y − z) + zx(z − x)

(3) x²y(x + y) + y²z(y + z) + z²x(z + x)

(4) x³(x + y) + y³(y + z) + z³(z + x)

(5) xy²(x − y) + yz²(y − z) + zx²(z − x)

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If x=49,y=−712 and z=−23, then verify that x−(y−z)≠(x−y)−z.

x=49,y=−712,z=−23 then x−(y−2)≠(x−y)−z⇒49−[−712−(−23)]≠[49−(−712)]−(−23)⇒49−[−712+23]≠[49+712]−(−23)⇒49−[−7+812]≠[16+2136]+23⇒49−112≠3736+23⇒16−336≠37+24361336≠6136 provedL.H.S and R.H.S are not equal

If $x = \frac{4}{9}, y = \frac{- 7}{12}$ and $z = \frac{- 2}{3}$ , then verify that $x - (y - z) \neq (x - y) - z$ .