Types of Inequalities

In the following questions, the symbols $, @, #, δ and * are used with the following meaning as illustrated below:
'P $ Q' means 'P is not smaller than Q'.
'P @ Q' means 'P is neither smaller than nor equal to Q'.
'P # Q' means 'P is neither greater than nor equal to Q'.
'P δ Q' means 'P is neither greater than nor smaller than Q'.
'P * Q' means 'P is not greater than Q'.
Now in each of the following questions assuming the given statements to be true, find which of the four conclusions I, II, III and IV given below them is/are definitely true and give your answer accordingly.

Statements: R * D, D $ J, J # M, M @ K
Conclusions:
I. K # J II. D @ M
III. R # M IV. D @ K

In each question below is given a statement followed by two conclusions numbered I and II. You have to assume everything in the statement to be true, then consider the two conclusions together and decide which of them logically follows beyond a reasonable doubt from the information given in the statement.

Statement: K$\ge$P, M$>$J, C$=$P, K$=$J

Conclusions: I. C$=$K
                     II. K$>$C

In the following questions, the symbols, $@$,$\#$,$\$$$\%$,$*$ are used with the following meanings:
A$@$B means A is not smaller than B.
A$\#$B means A is not smaller or equal to B
A$\$$B means A is not greater or equal to B
A$\%$B means A is neither greater nor smaller than B
A$*$B means A is not greater than B
In each of the following questions, assuming the given statements to be true, find which of the following options holds true: Give answer—
($1$) if only conclusion I is true.
($2$) if only conclusion II is true.
($3$) if either conclusion I or conclusion II is true.
($4$) if neither conclusion I nor conclusion II is true
($5$) if both conclusions I and II are true.

Statements: C$\$$R, M$@$U, C$@$P, P$\#$U
Conclusions: I. R$\#$U II. C$\#$U

In the following questions, the symbols $>,=,\ge ,$ and $<$ are used with the following meaning.

A$>$B means A is neither greater than nor smaller than B.
A$\ge$B means A is not greater than B.
A$<$B means A is neither smaller than nor equal to B.
A$=$B means A is neither greater than nor equal to B.
Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II have given them is/are definitely true. Given answer
($1$) If only conclusion I is true. 
($2$) If only conclusion II is true.
($3$) If either conclusion I or II is true.
($4$) If neither conclusion I nor II is true.
($5$) If both conclusions I and II are true.

Statements: M$<$A, V$>$M, S$\ge$V
Conclusion:

I. A$<$S

II. S$<$A

In this question relationship between different elements is shown in the statements. These statements are followed by two conclusions.

Statements : P > Q = R > S < T = U, V > W = S > X > Y = Z
Conclusions : $\mathrm{I}$. P > Z  $\mathrm{II}$. P > X

In the following questions, the symbols $@$, $\copyright$, $\$$, $\%$ and $\#$ are used with the following meaning as illustrated below:
'Z$\copyright$X' means 'Z is neither greater than nor equal to X'.
'Z$\%$X' means 'Z is neither smaller than nor greater than X'.
'Z$\$$X' means 'Z is not greater than X'.
'Z$@$X' means 'Z is neither smaller than nor equal to X'.
'Z$\#$X' means ' Z is not smaller than X'.
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: Z$@$U, D$\copyright$F, U$\$$D, F$\%$Y, Y$@$B
Conclusions: I. F$@$Z II. F$\%$U

In the following questions, the symbols $@$,$\#$,$\$$,$\%$, $*$ are used with the following meanings:
A@B means A is not smaller than B.
A#B means A is greater than B.
A$B means A is smaller than B.
A%B means A is neither greater nor smaller than B.
A*B means A is not greater than B.
In each of the following questions, assuming the given statements to be true, find which of the following options holds true:
Give answer—
($1$) if only conclusion I is true.
($2$) if only conclusion II is true.
($3$) if either conclusion I or conclusion II is true.
($4$) if neither conclusion I nor conclusion II is true
($5$) if both conclusions I and II are true.

Statements: Q$\%$L, C$\$$O, Q$\$$O, U$*$C
Conclusions: I. Q$\#$C II. O$\#$U

Study the following information carefully and answer the questions given below.

In a certain code, the symbol for,  $0$ is $\copyright$ and for, $1$ is $@$. There are no other symbols for all other numbers greater than, $1$. The numbers greater than $1$ are to be written only by using the two symbols given above. The value of the symbol for 1 doubles itself every time it shifts one place to the left. Study the following examples -
$0$ is written as $\copyright$
$1$ is written as $@$
$2$ is written as $@$ $\copyright$
$3$ is written as $@@$
$4$ is written as $@ \copyright \copyright$ and so on....................

Which of the following will represent $30\%$ of $120$ in that code?

In the following questions, the symbols, $@$, $\copyright$, $\$$, $\%$ and $\#$ are used with the following meaning as illustrated below:
'Z$\copyright$X' means 'Z is neither greater than nor equal to X'.
'Z$\%$X' means 'Z is neither smaller than nor greater than X'.
'Z$\$$X' means 'Z is not greater than X'.
'Z$@$X' means 'Z is neither smaller than nor equal to X'.
'Z$\#$X' means ' Z is not smaller than X'.
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: B$\copyright$U, L$\copyright$W, Y$\%$U, W$\$$C, U$@$L
Conclusions: I. C$\#$L II. C$\copyright$W

In the following questions, the symbols $@$, $\copyright$, $\$$, $\%$ and $\#$ are used with the following meaning as illustrated below:
'Z$\copyright$X' means 'Z is neither greater than nor equal to X'.
'Z$\%$X' means 'Z is neither smaller than nor greater than X'.
'Z$\$$X' means 'Z is not greater than X'.
'Z$@$X' means 'Z is neither smaller than nor equal to X'.
'Z$\#$X' means ' Z is not smaller than X'.
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: B$\$$T, N$\#$A, J$@$Y, T$\copyright$N, A$\%$Y
Conclusions: I. N$\%$J II. N$\#$B

In the following questions the symbols $@, +, \copyright , \$, △ \mathrm{and} ?$, are used with the following meaning:
'P$△$Q' means 'P is not equal to Q'.
'P$@$Q' means 'P is greater than Q'.
'P$+$Q' means 'P is smaller than Q'.
'P$\copyright$Q' means 'P is either greater than or equal to Q'.
'P$\$$Q' means 'P is either smaller than or equal to Q'.
'P$?$Q' means 'P is equal to Q'.
Now each of the following questions assuming the given statements to be true, find which of the two conclusions $\mathrm{I} \mathrm{and} \mathrm{II}$, given them is/are definitely true. Give answer.

Statements: D $@$ B, B $\$$ T, T $+$ M
Conclusions: $\mathrm{I}$. M $@$ B $\mathrm{II}$. T $\copyright$ B

In the following questions, the symbols , $@$, $\#$, $\$$, $\%$, $*$ are used with the following meanings:
A$@$B means A is not smaller than B.
A$\#$B means A is not smaller or equal to B
A$\$$B means A is not greater or equal to B
A$\%$B means A is neither greater nor smaller than B
A$*$B means A is not greater than B
In each of the following questions, assuming the given statements to be true, find which of the following options holds true: Give answer—
($1$) if only conclusion I is true.
($2$) if only conclusion II is true.
($3$) if either conclusion I or conclusion II is true.
($4$) if neither conclusion I nor conclusion II is true
($5$) if both conclusions I and II are true.

Statements: M$\#$R, O$*$N, M$@$N, O$\%$Q
Conclusions: I. N$\%$R II. R$\#$Q

In the following questions, the symbols $>$, $=$,$\ge$ and $<$ are used with the following meaning.

A$>$B means A is neither greater than nor smaller than B.
A$\ge$B means A is not greater than B.
A$<$B means A is neither smaller than nor equal to B.
A$=$B means A is neither greater than nor equal to 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 them is/are definitely true. Given answer
($1$) If only conclusion I is true. 
($2$) If only conclusion II is true.
($3$) If either conclusion I or II is true.
($4$) If neither conclusion I nor II is true.
($5$) If both conclusion I and II are true.

Statements: P$=$E , Q$\ge$P
Conclusions: I. E$<$P , II. E$>$P

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.

A$*$B means A is less than B.

A$\#$B means A is greater than B.

A and B means A is equals to B.

A$+$B means A is less than or equals to B.

A$\%$B means A is greater than or equals to B

.Give answer

$1$. If only conclusion I is true.

$2$. If only conclusion II is true.

$3$. If either conclusion I or II is true.

$4$. If neither conclusion I nor II is true.

$5$. If both conclusions I and II are true.

Statement: R$*$M, Land M, L$\%$N, N$\#$P
Conclusions I. R $\%$ N II. M$+$N

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.

A$*$B means A is less than B.

A$\#$B means A is greater than B.

A and B means A is equals to B.

A$+$B means A is less than or equals to B.

A$\%$B means A is greater than or equals to B

To Give answer: 

$1$. If only conclusion I is true.

$2$. If only conclusion II is true.

$3$. If either conclusion I or II is true.

$4$. If neither conclusion I nor II is true.

$5$. If both conclusions I and II are true.

Statement: N$\#$L, L$*$K, K$+$P, P$\%$J
Conclusions: I. N$+$P II. L$\%$J

Directions- In each of the following questions the symbols $\mathrm{\alpha }, \mathrm{\beta }, \mathrm{\gamma }, \mathrm{\delta }$ and $\mathrm{\varphi }$ have been used having their meaning as-
$\mathrm{M} \mathrm{\alpha } \mathrm{N}$ means M is greater than N.
$\mathrm{M} \mathrm{\beta } \mathrm{N}$ means M is smaller than N.
$\mathrm{M} \mathrm{\gamma } \mathrm{N}$ means M is not greater than N.
$\mathrm{M} \mathrm{\delta } \mathrm{N}$ means M is not shorter than N.
$\mathrm{M} \mathrm{\varphi } \mathrm{N}$ means M is equal to N.
Assuming the statement given in each of the following questions as true, deduce, which of the given five alternatives is definitely true ?

Statement- 
$\mathrm{F} \mathrm{\delta } 4\mathrm{H}, 2\mathrm{H} \mathrm{\varphi } 3\mathrm{J}$

In the following questions the symbols $@$, $\copyright$, $\$$, $\%$ and $\#$ are used with the following meaning as illustrated below:

Z$\copyright$X means Z is neither greater than nor equal to X.

Z$\%$X means Z is neither smaller than nor greater than X.

Z$\$$X means Z is not greater than X.

Z$@$X means Z is neither smaller than nor equal to X.

Z$\#$X means  Z is not smaller than X.

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.

Give answer

$1$. If only conclusion I is true.

$2$. If only conclusion II is true.

$3$. If either conclusion I or II is true.

$4$. If neither conclusion I nor II is true.

$5$. If both conclusions I and II are true.

Statements: 2$@$4, 3$\copyright$6, 4$\$$3, 6$\%$7, 7$@$8
Conclusions: I. 6$@$2 II. 6$\%$4

In the following questions, the symbols $@$,$\#$, $\$$, $\%$, $*$ are used with the following meanings:
A$@$B means A is not smaller than B.
A$\#$B means A is greater than B.
A$\$$B means A is smaller than B.
A$\%$B means A is neither greater nor smaller than B.
A$*$B means A is not greater than B.
In each of the following questions, assuming the given statements to be true, find which of the following options holds true:
Give answer—
($1$) if only conclusion I is true.
($2$) if only conclusion II is true.
($3$) if either conclusion I or conclusion II is true.
($4$) if neither conclusion I nor conclusion II is true.
($5$) if both conclusions I and II are true.

Statements: C$@$R, T$\%$I, Y$\$$C, T$*$R
Conclusions: I. R$\#$T II. Y$\#$T

In the following questions, assuming the given statements to be true, find which of the two conclusions I and II given them is/are definitely true.
Given answer
($1$) If only conclusion I is true.
($2$) If only conclusion II is true.
($3$) If either conclusion I or II is true.
($4$) If neither conclusion I nor II is true.
($5$) If both conclusion I and II are true.

Statements:
A$>$B,
B$\ge$C,
C$<$D
Conclusion:
I. A$>$C
II. A$=$C

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

Statements: H $\#$ M, N $\copyright$ D, X $\$$ N, V $\copyright$ X, D $\%$ H

Conclusions: $\mathrm{I}$. V $\%$ H $\mathrm{II}$. V $\copyright$ D $\mathrm{III}$. X $\copyright$ D