Symbols and Notations : Logical Reasoning

  • 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 – B' means 'A is father of B'
    ( IV ) 'A + B' means 'B is sister of A'
  • 1. 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.

  • 2. 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.

  • Instructions (3 - 4) :-
    Thease questions are based on the following information.
    ( I ) 'A * B' means 'A is father of B'
    ( II ) 'A – B' means 'A is sister of B'
    ( III ) 'A + B' means 'A is mother of B'
    ( IV ) 'A/B' means 'A is sister of B'
  • 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 

  • 4. 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 : (5 - 7) -
    In the following questions, the Symbols @, ©, $ , % and & are used with the following meanings as illustrated below.
    ‘A $ B’ means ‘A is not greater than B’.
    'A @ B' means 'A is neither smaller then nor equal to B'.
    'A & B' means 'A is neither greater than nor equal to B'.
    'A © B' means 'A is neither greater than nor smaller than B'.
    'A % B' means 'A is not smaller than 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: 
    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 )

  • 6. 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 ) 

  • 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 

  • Instructions : -(8 - 10)
    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 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 definitely true.
  • 8. 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) 

  • 9. 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) 

  • 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 )



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