Question

In Question some relationship have been expressed through symbols as defined below :
     \[\begin{align}
  & +-\times \div =>< \\
 & V\Lambda \left( {} \right)\bigcup \cap O \\
\end{align}\]
     In question only one of the five relationships is correct. Find the correct one and encircle its serial number on the space provided against the question\[\]

A.$24\cap 3\left( 4V2 \right)8$ \[\]
B. $24\bigcup 3V4\Lambda \left. 2 \right)8$ \[\]
C. $24\left( 3O4 \right)2V8$ \[\]
D. $24O3\left( 4 \right.\Lambda 28$ \[\]
E. $24\Lambda 3V4\bigcup 2V8$ \[\]

Answer 1

Hint: We see that the new symbols written below represent the arithmetic operation that is written right above for example, $V$is written for $'+'$. Replace the new symbols in each option to operation symbols and use the BODMAS rule to check the correctness. The BODMAS rule is the acronym for order of arithmetic operations which means we have to simplify bracket, order, division, multiplication, addition and subtraction in order.
Complete step-by-step answer:
The given new representation of relationship between two list of symbols is
\[\begin{align}
  & +-\times \div =>< \\
 & V\Lambda \left( {} \right)\bigcup \cap O \\
\end{align}\]
It means the symbols of arithmetic operations written in the first line above $+,-,\times ,\div ,=,>,<$ are represented with new symbols written in the line below $V,\Lambda ,\left( , \right),\bigcup ,\cap ,O$ respectively. \[\]

Checking option-A\[\]
The given expression is $24\cap 3\left( 4V2 \right)8$. We write the expression in symbols for arithmetic operation we get as $24\times 3+4\div 2>8$. We simplify with BODMAS rule and get
\[\begin{align}
  & 24\times 3+4\div 2>8 \\
 & \Rightarrow 72+2>8 \\
 & \Rightarrow 74>8 \\
\end{align}\]
So the option is correct. \[\]
Checking option-B\[\]
The given expression is $24\bigcup 3V4\Lambda \left. 2 \right)8$. We write the expression in symbols for arithmetic operation we get as $24\times 3=4\div 2+8$. We simplify with BODMAS rule and get
\[\begin{align}
  & 24\times 3=4\div 2+8 \\
 & \Rightarrow 72=10 \\
\end{align}\]
So the option is not correct.\[\]
Checking option-C\[\]
The given expression is $24\left( 3O4 \right)2V8$. We write the expression in symbols for arithmetic operation we get as $24\div 3+4<2=8$. So the option is not correct because the symbols of equality and inequality cannot lie in the same expression. \[\]

Checking option-D\[\]
The given expression is $24O3\left( 4 \right.\Lambda 28$. We write the expression in symbols for arithmetic operation we get as $24-3\div 4=2\times 8$. We simplify with BODMAS rule and get
\[\begin{align}
  & 24-3\div 4=2\times 8 \\
 & \Rightarrow 23.25=16 \\
\end{align}\]
So the option is not correct. \[\]
Checking option-E\[\]
The given expression is $24\Lambda 3V4\bigcup 2V8$. We write the expression in symbols for arithmetic operation we get as $24\div 3>4+2\times 8$. We simplify with BODMAS rule and get

\[\begin{align}
  & 24\div 3>4+2\times 8 \\
 & \Rightarrow 8>16 \\
\end{align}\]
So the option is not correct. \[\]

So, the correct answer is “Option A”.

Note: It is better to write symbols side by side in rough paper before solving. The BODMAS rule used for order of operations is also called PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction ) rule. The O in BODMAS means order which is another word for exponent.