Symbols and Notations : Logical Reasoning

1.

Statements: 
D % H, H $ P, P @ Q 
Conclusions: 
I .D @ P 
II. Q & H

   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

Answer: Option 'D'

D & H -> D = H 
H $ P -> H = P 
P @ Q -> P > Q 
Therefore D = H = P > Q 
Conclusions: 
1. D @ P -> D > P ( Not True ) 

2.

Which of the following represents ‘ J is son of F ‘’ ?

   A.) J / R – T * F
   B.) J + R – T * F
   C.) J / M – N * F
   D.) None of these

Answer: Option 'D'

A.) J / R – T * F 
J + R means J is brother of R 
R - T means R is sister of T 
T * F means T is fother of F 
Therefore, J is Uncle of F 
B.) J + R means J is Mother of R 
J is a female. 
C.) J / M means J is brother of M 
M – N means M is sister of N 
N * F means N is father of F 
Therefore J is uncle of F.

  • Instructions (3 - 4) :-
    Thease questions are based on the following information.
    ( I ) 'A * B' means 'A is father of B'
    ( II ) 'A

3.

In the expression D + F * O / P, how is O related to D?

   A.) Grand daughter
   B.) Son
   C.) Grand son
   D.) Daughter

Answer: Option 'C'

D + F * O / P 
D + F means D is mother of F 
F * O means F is father of O 
O * P means O is brother of P 

  • Instructions : -(8 - 10)
    In the following questions, the Symbols @,

4.

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

Answer: Option 'B'

I)A $ B means A not a lessthan B Therefore, A = B 
II) A # B means A not a greater than B Therefore, A = B 
III) A @ B means A not a lessthan B and A ? B Therefore, A = B 
IV) A © B means A not a lessthan B and A !> B Therefore, A = B 
V ) A % B means A not a greater than B and A ? B Therefore, A < 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) 

5.

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.) All are true

Answer: Option 'D'

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) 

  • Instructions : (5 - 7) -
    In the following questions, the Symbols @,

6.

Statements: 
C & D, D $ E, E © F 
Conclusions: 
I .F @ C 
II. E @ C

   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 both conclusions I and II are true.

Answer: Option 'D'

‘A $ B’ -> A !> B, therefore A = B. 
‘A @ B’ -> A B. 
‘A & B’ -> A !> B and A ‘A © B’ -> A !> B and A ‘A % B’ -> A C & D -> C < D 
D $ E -> D = E 
E © F -> E = F 
Therefore C < D = E = F 
Conclusions: 
1. F @ C -> F > C ( True ) 
2. E @ C -> E > C ( True )

7.

Statements: 
A © B, B % C, C & D 
Conclusions: 
I. C & A 
II. C © A

   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

Answer: Option 'C'

A © B -> A = B 
B % C -> B = C 
C & D -> C < D 
Therefore A = B = C < D 
Conclusions: 
1. C & A -> C < A ( Not True ) 
2. C © A -> C = A ( Not True ) 
C is either smaller than or equal to A. Therefore, either conclusion I or conclusion II is follows 

8.

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.) None is true

Answer: Option 'D'

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) 

  • Instructions : -(11 - 12)
    In the following questions , 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

Answer: Option '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.

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

Answer: Option '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 )

  • Instructions (1-2) :-
    Thease questions are based on the following information.
    ( I ) 'A * B' means 'A is brother of B'
    ( II ) 'A / B' means 'B is mother of A'
    ( III ) 'A

11.

Which of the following means L is daughter of H?

   A.) L + K / J – H
   B.) H – J * R + L
   C.) L – J * H / K
   D.) L + W * R / H

Answer: Option 'B'

H – J * R + L 
L -> Sister R ,
R -> Brother J,
J -> Fother H 
Therefore, L is daughter of H.

12.

How is S related to T in the Expression: T / P + S ?

   A.) Daughter
   B.) Sister
   C.) Niece
   D.) Aunt

Answer: Option 'D'

T / P + S 
S -> Sister P ,
P -> Mother T 
Therefore, P is the mother of T and S is the sister of P. 
Then S is Aunt of T.


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