Types of Inequalities

In the questions given below, certain symbols @, ©, $, % and # are used with the following meaning : 'S $ L' means 'S is not greater than L'. 'S@L' means 'S is neither smaller than nor equal to L'. 'S # L' means 'S is not smaller than L'. 'S © L' means 'S is neither greater than nor equal to L'. 'S % L' means 'S is neither smaller than nor greater than L'. 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.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: G#L , F@X, L$F, B%X
Conclusions: I. F@B II. G@B

In the following questions, the symbols, $\#, \$, \copyright , @$ and $\%$, are used with the following meaning as illustrated below:
'P $\#$ Q' means 'P is neither greater than nor equal to Q'.
'P $@$ Q' means 'P is neither greater than nor smaller than Q'.
'P $\$$ Q' means 'P is not smaller than Q'.
'P $\copyright$ Q' means 'P is neither smaller than nor equal to Q'.
'P $\%$ Q' means 'P is not greater than Q'
Statements: M $\copyright$ R, R $\%$ T, T $@$ N
Conclusions: $\mathrm{I}$. N $\copyright$ R $\mathrm{II}$. N $@$ R

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 the following questions, the symbols $@, \#, \$, \%$ and $\copyright$, are used with the following meaning as illustrated below:
'P $\$$Q' means 'P is not greater than Q'.
'P $@$ Q' means 'P is neither smaller than nor equal to Q'.
'P $\%$ Q' means 'P is neither greater than not equal to Q'.
'P $\copyright$ Q' means 'P is not smaller than Q'.
'P $\#$ Q' means 'P is neither greater than nor smaller than Q'.
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.

Statements: V $\copyright$ M, N $\%$ V, J $@$ N
Conclusions: $\mathrm{I}$. J$@$  M $\mathrm{II}$. M $@$ N $\mathrm{III}$. V $@$ J

In the questions given below, certain symbols are used with the following meanings:
P$\#$Q means P is neither equal to nor smaller than Q.
P$\%$Q means P is not smaller than Q.
P$\$$Q means P is neither greater nor smaller than Q.
P and Q means P is neither greater than nor equal to 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 two conclusions I and ii given below them is / are definitely true.
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 and II are true.
($5$) If both conclusions I and II are true.

Statements:
Y$\$$Z, B$\#$A,
Y and A
Conclusions:
I. A$\#$Z
II. Y and B

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 given question made with alphabets and certain symbols with the following meanings:
'A $@$ B' means 'A is greater than B'.
'A $*$ B' means 'A is either greater than or equal to B'.
'A $\#$ B' means 'A is equal to B'.
'A $\$$ B' means 'A is either smaller than or equal to B'.
'A $+$ B' means 'A is smaller than B'.

Answer the following statements using the given conditions --
Statements: P $\$$ Q, N $\#$ M, M $@$ R, R $*$ P
Conclusions:
I. P $+$ N
II Q $\$$ M

In the question given below, some symbols $@, \%, \$, \copyright$ and $\#$ are used with the following meaning as illustrated below :
$\mathrm{A}@\mathrm{B}$ means $\mathrm{A}$ is not greater than $\mathrm{B}$.
$\mathrm{A}\%\mathrm{B}$ means $\mathrm{A}$ is not smaller than $\mathrm{B}$.
$\mathrm{A}\$\mathrm{B}$ means $\mathrm{A}$ is neither smaller than nor greater than $\mathrm{B}$.
$\mathrm{A}\copyright \mathrm{B}$ means $\mathrm{A}$ is neither greater than nor equal to $\mathrm{B}$.
$\mathrm{A}\#\mathrm{B}$ means $\mathrm{A}$ is neither smaller than nor equal to $\mathrm{B}$.
Now in each of the following question, 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: $\mathrm{VV}\copyright \mathrm{KK}, \mathrm{KK}\%\mathrm{DD}, \mathrm{DD}\$\mathrm{FF}$

Conclusions:

I. $\mathrm{VV}@\mathrm{DD}$

II. $\mathrm{FF}@\mathrm{KK}$

In the following given below, certain symbols are used with the following meanings:
'P $\$$ Q' means 'P is neither equal to nor smaller than Q'.
'P $\copyright$ Q' means 'P is not smaller than Q'.
'P $*$ Q' means 'P is neither greater nor smaller than Q'.
'P $\#$ Q' means 'P is neither greater than nor equal to Q'.
'P $@$ Q' means 'P is not greater than Q'.

Statements: R $\copyright$ P, P $\$$ M, M $@$ D
Conclusions: $\mathrm{I}$. D $\$$ R $\mathrm{II}$. M$\#$  R

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

'$\mathrm{P}\copyright \mathrm{Q}$' means 'P' is greater than 'Q'.
'$\mathrm{P}\%\mathrm{Q}$' means 'P' is smaller than 'Q'.
'$\mathrm{P}@\mathrm{Q}$' means 'P' is either greater than or equal 'Q'.
'$\mathrm{P}\$\mathrm{Q}$' means 'P' is either smaller than or equal to 'Q'.
'$\mathrm{P}\#\mathrm{Q}$' means 'P' is equal to 'Q'.

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

A) If only conclusion I is true.
B) If only conclusion II is true.
C) If either conclusion I or II is true.
D) If neither conclusion I nor II is true.
E) If both conclusions I and II are true

Statements: $\mathrm{T} \% \mathrm{J}, \mathrm{J} @ \mathrm{V}, \mathrm{V} \# \mathrm{W}$T % J, J @ V, V # W
Conclusions: I. $\mathrm{T}\copyright \mathrm{W}$II. $\mathrm{W}@\mathrm{T}$

In the following questions, the symbols $+$, $@$, $\copyright$, $\$$ and $∆$ are used with the following meaning as illustrated below:
$\mathrm{M}+\mathrm{N}$ means '$\mathrm{M}$ is not smaller than $\mathrm{N}$'.
$\mathrm{M}@\mathrm{N}$ means '$\mathrm{M}$ is neither smaller than nor equal to $\mathrm{N}$'.
$\mathrm{M}\copyright \mathrm{N}$ means '$\mathrm{M}$ is neither greater than nor equal to $\mathrm{N}$'.
$\mathrm{M}\$\mathrm{N}$ means '$\mathrm{M}$ is neither smaller than nor greater than $\mathrm{N}$'.
$\mathrm{M}∆\mathrm{N}$ means '$\mathrm{M}$ is not greater than $\mathrm{N}$'.
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 : $\mathrm{W}+\mathrm{R}, \mathrm{S}\$\mathrm{Z}, \mathrm{X}\copyright \mathrm{W}, \mathrm{S}∆\mathrm{R}$
Conclusions :

I. $\mathrm{R}\copyright \mathrm{S}$

II. $\mathrm{X}@\mathrm{S}$

In the following question, the symbols $@, \$, \%, \#$ and $\copyright$ are used with the following meanings illustrated.
'$\mathrm{A} @ \mathrm{B}$' means 'A is not smaller than B'.
'$\mathrm{A} \$ \mathrm{B}$' means 'A is not greater than B'.
'$\mathrm{A} \% \mathrm{B}$' means 'A is neither smaller than nor equal to B'.
'$\mathrm{A} \# \mathrm{B}$' means 'A is neither greater than nor equal to B'.
'$\mathrm{A} \copyright \mathrm{B}$' means 'A is neither smaller than nor greater than B'.
In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true.
Give answer—
A If only conclusion I is true.
B If only conclusion II is true.
C If either conclusion I or conclusion II is true.
D If neither conclusion I nor conclusion II is true.
E If both conclusions I and II are true.

Statements:
$\mathrm{E} \% \mathrm{F}, \mathrm{F} \# \mathrm{G}, \mathrm{G} @ \mathrm{H}$
Conclusions:
$\mathrm{I}. \mathrm{H} \# \mathrm{F} \mathrm{II}. \mathrm{E} \% \mathrm{G}$

In the question given below, some symbols *, ©, ð, $ and @ are used with the following meaning as illustrated below :
A*B means A<B
A©B means A > B
AðB means A = B.
A$B means A < B
A@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 : W δ K, K © F, F $ M
Conclusions :
I. M © K
II. W @ F
III. F @ W

Study the given instruction carefully --
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 $\$$ Q means P is neither greater nor smaller than Q.
P $\%$ Q means P is not greater than Q.
P $\&$ Q means P is not smaller than Q.

Which of the following conclusion is/are true, if assuming the given statements are true.
($1$) 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 is true.

Statements:
P  $\&$ Q,
Q $\%$ R,
R  $\$$ S
Conclusions:
I. Q $\$$ S
II. P $\#$ S

In these questions the symbols %, ©, ^, @ and # are used with different meanings as follows:
A % B means A is not greater than B.
A © B means A is neither greater than nor equal to B.
A ^ B means A is not smaller than B.
A @ B means A is neither smaller than nor equal to B.
A # B means A is neither greater than nor smaller than B.
Now in each of the following questions assuming the given statements to be true, find out which of the conclusions I, II, III given below them is/are definitely true and mark your answer accordingly.

Statements:
A % B,
B ©C,
D @ C,
D © E
Conclusions:
I. A © D
II. E @ C
III. B © D

In these questions, certain symbols have been used to indicate relationships between elements follows:
'A*B' means 'A is either equal to or greater than B'.
'A$B' means 'A is equal to B'.
'A£B' means 'A is either equal to or smaller than B'.
'A&B' means 'A is smaller than B'.
'A@B' means 'A is greater than B'.

Statements: Y $ Z, H $ D, Z * D
Conclusions: 1. D £ Y II. H £ Z

In the following question, assuming the given statements to be true, find which of the two conclusions $\mathrm{I}$ and $\mathrm{II}$ given below is/are definitely true.

Give answer.
$1.$ If only conclusion $\mathrm{I}$ is true.
$2.$ If only conclusion $\mathrm{II}$ is true.
$3.$ If either conclusion $\mathrm{I}$ or $\mathrm{II}$ is true.
$4.$ If neither conclusion $\mathrm{I}$ nor $\mathrm{II}$ is true.
$5.$ If both conclusions $\mathrm{I}$ and $\mathrm{II}$ are true.

Statement: M $<$ N $>$ O $>$ P $<$ R $>$ S

Directions- In each of the following questions the symbols $\left(\mathrm{\alpha }\right), \left(\mathrm{\beta }\right), \left(\mathrm{\gamma }\right), \left(\mathrm{\delta }\right)$ and $\left(\mathrm{\varphi }\right)$ have been used having their meaning as-
$\mathrm{M}\left(\mathrm{\alpha }\right)\mathrm{N}$ means M is greater than N.
$\mathrm{M}\left(\mathrm{\beta }\right)\mathrm{N}$ means M is smaller than N.
$\mathrm{M}\left(\mathrm{\gamma }\right)\mathrm{N}$ means M is not greater than N.
$\mathrm{M}\left(\mathrm{\delta }\right)\mathrm{N}$ means M is not shorter than N.
$\mathrm{M}\left(\mathrm{\varphi }\right)\mathrm{N}$ 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-
$\mathrm{B}\left(\mathrm{\varphi }\right)3\mathrm{C}, 4\mathrm{C}\left(\mathrm{\gamma }\right)\mathrm{A}$

In the following questions some symbols @, ©, $, % and # are used with the following meaning as illustrated below:
'A @ Z' means 'A is neither greater than nor equal to Z'.
'A © 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 I, II and III given below them is/are definitely true and give your answer accordingly.

Statements: P $ M, Q % N, N © P, T @ Q, M % Z

Conclusions: I. N © M II. T @ N III. Z $ Q

Some relationships have been expressed through symbols which are explained below:

X = greater than
? = not less than
# = not equal to
^ = equal to
+ = not greater than
@ = less than

If a X b @ c, which of the following must be true?