**In the following questions(1-4), the symbol × , ∂ , % , © , @ , are used with the following illustrations.**

P % Q means P is not smaller than Q

P © Q means P is neither smaller than nor equal to Q

P x Q means P is neither greater than nor equal to Q

P ∂ Q means P is not greater than Q

P @ Q means P is neither greater than nor smaller than Q

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1. Statement – R ∂ K ; K x M ; M @ J

Conclusions -:

I. J © K

II. M © R

III. R X J

A. Only I & I are true

B. Only II & III are true

C. Only I & III are true.

D. All I, II & III are true

E. None of these

2. Statements – Z @ M ; M © K ; K X F

Conclusions – :

I. F © Z

II. K X Z

III. F © M

A. None is true

B. Only I is true

C. Only II is true

D. Only III is true

E. Only II & III are true.

3. Statements – V % H ; H @ F ; F ∂ E

Conclusions :-

I. F @ V

II. F X V

III. E % H

A. Only either I or II is true

B. Only III is true

C. Only I & II are true

D. All I, II & III are true.

E. Only either I or II and three are true.

4. Statements – W © T ; T ∂ N ; N % D

Conclusions :-

I. D X T

II. W © N

III. D @ T

A. None in True

B. Only I is true

C. Only II is true

D. Only III is true

E. Only I & II are true

**In the following questions(5-8), the Symbols @, ©, $ , % and # are used with the following meanings as illustrated below.**

‘A $ B’ means ‘A is not smaller than B’.

‘A # B’ means ‘A is not greater then B’.

‘A @ B’ means ‘A is neither smaller than nor equal to B’.

‘A © B’ means ‘A is neither smaller than nor greater than B’.

‘A % B’ means ‘A is neither greater than nor equal to B’.

In each of the following question assuming the given statements to be true, find out which of the two conclusions I and I I given below these are definitily true.

5.Statements: H % J, J © N, N @ R

Conclusions:

I. R % J

II. H @ J

III. N @ H

A. Only II is true

B. Only I and III are true

C. Only I is true

D. Only III is true

E. None of these

6. Statements: M @ J, J $ T, T © N

Conclusions:

I. N # J

II. T %M

III. M @ N

A. Only I and II are true

B. Only II and III are true

C. Only I and III are true

D. None of true

E. All are true

7.Statements: D © K, K # F, F @ P

Conclusions:

I. P @ D

II. K # P

III. F $ D

A. Only II is true

B. Only I and II are true

C. Only III is true

D. Only II and III are true

E. None of these

8.Statements: K # N, N $ T, T % J

Conclusions:

I. J @ N

II. K @ T

III. T @ K

A. Only I and II are true

B. Only II and III is true

C. Only I and III are true

D. None is true

E. None of these

**In the following questions(9-12) , the Symbols @, #, $ , % and * are used with the following meanings as illustrated below. **

‘A $ B’ means ‘A is not smaller than B’.

‘A % B’ means ‘A is not greater then 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’.

‘A # B’ means ‘A is neither greater than nor equal to B’.

In each of the following question assuming the given statements to be true, find out which of the three conclusions I,II and III given below them is/are definitily true.

9. Statements: D * Q, Q @ L, L $ B, B # G

Conclusions:

I. D @ B

II. B * D

III. G @ L

A. Either I or II only

B. I and II only

C.) I only

D. II and III only

E. None of these

10. Statements: Z @ Y, Y # K, K % M, M @ T

Conclusions:

I. Z @ M

II. Y @ T

III. Z # K

A. I only

B. II and III only

C. Either I or II only

D. All I,II and III

E. None of these

11.Statements: P # M, M % R, R * T, T # L

Conclusions:

I. P # M

II. P * R

III. M % L

A. I only

B. I and II only

C. Either I or III only

D. All I,II and III

E. None is true

12.Statements: F @ H, M % H, M $ R, G * M

Conclusions:

I. F $ R

II. F @ R

III. H $ G

A. I only

B. II and III only

C. Either I or III only

D. All I,II and III

E. None is true

**Answers with solutions**

P % Q means P is not smaller than Q —————– [ P≥ Q ]

P © Q means P is neither smaller than nor equal to Q — [ P > Q]

P x Q means P is neither greater than nor equal to Q ——— [ P < Q ]

P ∂ Q means P is not greater than Q ———- [ P ≤ Q ]

P @ Q means P is neither greater than nor smaller than Q——- [ P=Q ]

1. (D) Statement – R ∂ K ; K x M ; M @ J

R ≤ K < M = J

Conclusions -:

I. J © K ——- [ J > K ]

II. M © R —- [ M > R ]

III. R X J —— [ R < J ]

Clearly All the conclusions are true

2 -(C) Statements – Z @ M ; M © K ; K X F

Z = M > K < F

Conclusions – :

I. F © Z ———- [ F > Z ] cannot be said.

II. K X Z ——— [ K < Z ] Surely it is

III. F © M ——– [ F > M ] cannot be said

So Only II is correct.

3- (E)Statements – V % H ; H @ F ; F ∂ E

V ≥ H = F ≤ E

Conclusions :-

I. F @ V —- [ F=V ] not sure may nor may not be

II. F X V ——— [ F < V ] Not sure may or may not be

III. E % H ——- [ E ≥ H ] Surely.

But here F= H & H ≤ V so indirectly F≤V so either F= V or F < V but not both at a time, but atleast one has to hold. So either I or II should be there and III is always right. So answer is either I or II & III are correct.

4 -(A) Statements – W © T ; T ∂ N ; N % D

Means – W > T

N ≥ T

N ≥ D

Conclusions :-

I. D X T —– [ D < T ] cannot be said. No idea of relation between them

II. W © N — [ W > N ] cannot be said

III. D @ T — [ D = T ] cannot be said.

So here None is true.

A $ B means A not a lessthan B Therefore, A = B

A # B means A not a greater than B Therefore, A = B

A @ B means A not a lessthan B and A ? B Therefore, A = B

A © B means A not a lessthan B and A !> B Therefore, A = B

A % B means A not a greater than B and A ? B Therefore, A < B

5.(B) H % J = H < J

J © N = J = N

N @ R = N > R

Therefore, H < J = N > R

Conclusions:

I. R % J = R < J ( True )

II. H @ J =H > J ( Not true)

III. N @ J =N > H (True)

6.(E)

M % J = M > J

J $ T = J = T

T © N =T = N

Therefore, M > J = T = N

Conclusions:

I. N # J = N = J ( true )

II. T % M = T < M ( true)

III. M @ N =M > N ( true)

7.(C)

D © K -> D = K

K # F -> K = F

F @ P -> F > P

Therefore, D = K = F > P

Conclusions:

I. P @ D -> P > D ( Not true )

II. K # P -> K = P ( Not true )

III.F $ D -> F = D ( True )

8. (D)

K # N -> K = N

N $ T -> N = T

T % J -> T > J

Therefore, K = N = T > J

Conclusions:

I. J @ N -> J > N ( Not true )

II. K @ T -> K > T ( Not true )

III.T @ K -> T > K ( Not true )

9. (C)

Statements D * Q -> D = Q

D @ L -> Q > L

L $ B -> L = B

B # G -> B < G

Therefore, D = Q > L = B < G

Conclusions:

I. D @ B -> D > B ( True )

II. B * D -> B = D ( Not true)

III.G @ L -> G < L (Not true)

10.(E)

Statements: Z @ Y -> Z > Y

Y # K -> Y < K

K % M -> K = M

M @ T -> M > T

Therefore, Z > Y < K = M > T

Conclusions:

I. Z @ Y -> Z > Y (Not true )

II. Y @ T -> Y > T ( Not true)

III.Z # K -> Z < K (Not true)

11.(A)

Statements: P # M -> p < M

M % R -> M = R

R * T -> R = T

T # L -> T < L

Therefore, P < M = R = T < L

Conclusions:

I. P # R -> P < R ( true )

II. P * R -> P = R ( Not true)

III. M % L -> M = L (Not true)

12.(B)

Statements: F @ H -> F > H

M % H -> M = H

M $ R -> M = R

G * M -> G = M

Therefore, G > H = M = G = R

Conclusions:

I. F $ R -> F = R (Not true )

II. F @ R -> F > R ( true)

III.H $ G -> H = G ( true)