Introduction to Linear Inequations

In the following questions, the symbols,$\#, *, @, \$$ and $=$are used with the following meaning as illustrated below: $\mathrm{A} \# \mathrm{B}$ means A is neither greater than nor equal to $\mathrm{B}$. $\mathrm{A}*\mathrm{B}$ means A is not greater than $\mathrm{B}$. $\mathrm{A} @ \mathrm{B}$ means $\mathrm{A}$ is equal to $\mathrm{B}$.$\mathrm{A} \$ \mathrm{B}$ means A is neither less than nor equal to $\mathrm{B}$. $\mathrm{A}=\mathrm{B}$ means $\mathrm{A}$ is not less than $\mathrm{B}$. Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true and give your answer accordingly.

Statements:
$\mathrm{W}@\mathrm{Y}, \mathrm{Y} \#\mathrm{P}=\mathrm{Q}, \mathrm{Q}*\mathrm{X}$

Conclusions:
I. $\mathrm{W}=\mathrm{Q}$
II. $\mathrm{W}\#\mathrm{Q}$

In the questions given below, some symbols *, $, @, %, $\copyright$ are used with the following meaning as illustrated below:
A * B means A < B
A $ B means A > B
A @ B means A = B
A % B means A < B
A$\copyright$B means A > B

Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below is/are definitely true? Give answer.

Statements:
E@D, D%C, C*B, B$A

Conclusions:
I. A$C   II. B$\copyright$E    III. D%B    IV. B@D

The set of values of $k\left(k\in R\right),$ for which the equation $x^2-4\left|x\right|+3-\left|k-1\right|=0$ will have exactly four real roots is 

If $x$and $y$ are rational numbers then $\left|x+y\right|$ is 

Which of the following is not an example of 'slack inequality' ?

Which of the following is an example of 'strict inequality' ?

Which of the following is an example of literal inequality ?

Which one of the following is a numeral Inequality ?

Identify the slack inequality from the given alternates. 

Identify the slack inequality from the given alternates. 

Identify the strict inequality from the given alternates. 

Identify the strict inequality from the given alternates. 

Identify the double inequality from the given alternates. 

Identify the double inequality from the given alternates. 

Identify the literal inequality from the given alternates. 

Identify the literal inequality from the given alternates. 

Identify the numeral inequality from the given alternates. 

Identify the numeral inequality from the given alternates. 

If $\mathrm{a}$ and $\mathrm{b}$are negative, and $\mathrm{c}$ is positive, then which of the following statement(s) is/are true?
$\mathrm{I}$$\mathrm{a}-\mathrm{b}<\mathrm{a}-\mathrm{c}$
$\mathrm{II}$If $\mathrm{a}<\mathrm{b}$, then $\mathrm{a} / \mathrm{c}<\mathrm{b} / \mathrm{c}$
$\mathrm{III}$ $\mathrm{a} / \mathrm{b}<\mathrm{a} / \mathrm{c}$

Which of the following are Literal Inequalities?