Question

$\huge\underbrace{\purple{Q}\orange{u}\red{e}\pink{s}\blue{t}{i}\blue{o}\green{n}}$


question in above attachment
don't spam
and don't copy from google ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

⊙ TO DETERMINE

In Boolean Algebra the complement of ( a.b + a.c )

⊙ PROPERTY TO BE IMPLEMENTED

1. DISTRIBUTIVE PROPERTY

$\sf{a.(b + c) = a.b + a.c \: }$

2. DE MORGAN'S LAW

$\sf{(i) \: \: \: \: (a.b) '=a' + \: b'}$

$\sf{(ii) \: \: \: \: (a+b) '=a'. \: b'}$

⊙ CALCULATION

$\sf{The \: complement \: of \: \: ( a.b + a.c )}$

$= \sf{ ( a.b + a.c ) ' \: }$

$= \sf{[ \: a.(b +c ) \: ] '} \: \: \: ( \: using \: property \: 1 \: )$

$= \sf{[ \: a ' + (b +c ) '} \: ]\: \: ( \: using \: property \: 2(i)\: )$

$= \sf{ \: a ' + ( \: b' .c ' \: )} \: \: \: ( \: using \: property \: 2(ii)\: )$

⊙ RESULT

$\boxed{ \sf{ \: \: \: ( a.b + a.c ) ' \: = \: a ' + ( \: b' .c ' \: ) \: \: \: }}$

━━━━━━━━━━━━━━━━

Answer 2

Explanation:

Given :

Area of rhombus = 120 cm²

Length of diagonal = 8 cm

To find :

Length of another diagonal

According to the question,

$\sf{ : \implies Area \: of \: rhombus = \dfrac{1}{2} \times d _{1} \times d_{2} }$

$\sf : \implies{ {120 \: cm}^{2} = \dfrac{1}{2} \times 8 \: cm \times x}$

$\sf : \implies{ {120 \: cm}^{2} \times 2 = 8 \: cm \times x }$

$\sf : \implies{ {240 \: cm}^{2} = 8 \: cm \times x}$

$\sf : \implies{ \dfrac{240}{8} \: cm = x}$

${ \underline{ \boxed{ \sf \pink{ : \implies{ \bm3 \bm0 \: c m =x}}}}}$

${ \therefore{ \underline{\sf{So \:,the \: length \: of \: other \: diagonal \: is \: 3 0 \: cm}}}}$